Exhibit 10.1

FORBEARANCE AND NOTE PAYMENT AMENDMENT AGREEMENT

This Forbearance and Note Payment Amendment Agreement (“Agreement”) is made and entered into this 6th day of May 2026 (the “Effective Date”), by and between, J.J. ASTOR & CO., a Utah corporation (the “Lender”), and VIVAKOR, INC., a Nevada corporation (“Vivakor” or the “Company”). The Company and the Lender are sometimes referred to collectively as the “Parties.”

RECITALS

WHEREAS, on March 17, 2025, the Company and the Lender entered into a loan agreement, as amended on June 17, 2025, July 9, 2025, and February 27, 2026 (the “Loan Agreement”); and

WHEREAS, on July 9, 2025, the Company issued the Lender a $5,940,000 principal amount amended and restated convertible installment secured promissory note (the “Second Note”), of which $6,815,805.71 is currently outstanding, due and payable as of the Effective Date of this Agreement; and

WHEREAS, as a result of the Company’s failure to make the payments required to be made under the Second Note and the Second Forbearance Agreement, on February 5, 2026, the Company and the Lender entered into a fourth Forbearance, Note Payment and Registration Rights Amendment Agreement (the “Fourth Forbearance Agreement”), pursuant to which (i) the interest rate under the Second Note was reduced to nine percent (9%) per annum, compounded daily, (ii) the Maturity Date of the Second Note was extended to as late as January 1, 2027, and (iii) the Parties established and agreed upon the “Second Note Amended Repayment Terms” (as defined in the February 5, 2025 Amendment); and

WHEREAS, pursuant to the Fourth Forbearance Agreement on February 5, 2026, the Company and the Lender amended the terms of the Second Note such that (a) the Maturity Date of the Second Note was extended to as late as January 1, 2027, and (b) the Company agreed to pay the outstanding balance of the Second Note in the following installments, with payments, payable, at the option of the Company, either in cash or under certain conditions in Conversion Shares issued at the Default Conversion Price that are immediately salable by the Lender under Rule 144, as follows: (i) $50,000 per week commencing Monday, April 6, 2026, (ii) $100,000 per week commencing Monday, July 6, 2026, (iii) $150,000 per week commencing Monday, October 5, 2026, and (iv) $250,000 per week commencing Monday, December 7, 2026, with the outstanding balance to be paid in full by January 1, 2027 (the “Second Note Amended Repayment Terms”); and

WHEREAS, the Company failed to make the first required payment due April 6, 2026, resulting in a new default under the Notes, as a result of which default (i) the amount due and payable under the Second Note reverted back 120% of the $5,995,722.21 reduced amount that was previously due and payable under the Fourth Forbearance Agreement, (ii) the outstanding principal amount of the Second Note, as adjusted, increased to the Default Amount of one hundred ten percent (110%) of the then outstanding balance, and (iii) all interest under the Notes is calculated on the basis of a 360-day year for actual days elapsed, as a result of which $6,815,805.71 is currently outstanding, due and payable under the Second Note as of the Effective Date of this Agreement; and

WHEREAS, on February 27, 2025, the Company issued the Lender a $993,750 principal amount secured promissory note (the “Fourth Note”, and together the with Second Note, the “Notes”), of which $1,111,151.74 is outstanding, due and payable as of the Effective Date of this Agreement, since the maturity date under the Fourth Note was April 6, 2026 and no payments have been received by the Lender; and

WHEREAS, the Fourth Note is secured by the collateral described therein and in the Loan Agreement and other Transaction Documents, and the Company hereby reaffirms, ratifies and confirms all existing security interests, liens, pledges, assignments, collateral rights and remedies in favor of the Lender, and further agrees that all such collateral, security interests and liens shall secure all obligations owing to the Lender under both the Second Note and the Fourth Note (collectively, the “Notes”), including all principal, accrued interest, default interest, costs, expenses and other amounts due; and

WHEREAS, the Company has failed to repay the Notes as required pursuant to the terms thereof, which defaults remain uncured as of the date hereof (collectively, the “Existing Defaults”); and

WHEREAS, the Company and Lender desire to extend the maturity date under the Fourth Note to July 15, 2026 (“Fourth Note Maturity Date”), reset the payment dates under the Notes as set forth in Section 2 below (the “Amended Repayment Terms”), and reduce the Interest Rate under the Notes during the Forbearance period only to nine percent (9%) compounded daily and calculated on the basis of a 360-day year for actual days elapsed, such that the Lender will forebear from exercising remedies with respect to the Existing Defaults only for so long as the Company strictly complies with this Agreement; and

WHEREAS, unless otherwise defined herein all capitalized terms when used in this Agreement shall have the same meanings as they are defined in the Loan Agreement and Notes.

NOW, THEREFORE, in consideration of the promises, mutual covenants, understandings and agreements contained in this Agreement, and other good and valuable consideration, the receipt and sufficiency of which are acknowledged by all parties, the parties do hereby agree as follows:

1. Extension of Maturity Date/Forbearance. During the Forbearance period only, interest shall accrue on the outstanding balance of the Notes at a rate of nine percent (9%) per annum, compounded daily and calculated on the basis of a 360-day year for actual days elapsed. Effective upon the Parties’ execution of this Agreement, the Parties agree that the maturity date under the Fourth Note will be the Fourth Note Maturity Date. The Lender agrees that, solely during the Forbearance period and only so long as the Company strictly complies with the Amended Repayment Terms and all other terms of this Agreement, it will not exercise any of its rights or remedies with respect to the Existing Defaults that pertain to the Notes through the Notes’ respective maturity dates, and the Lender will not exercise its conversion rights under the Notes through the Notes’ respective maturity dates (the “Forbearance”). The Company acknowledges that the $6,815,805.71 adjusted outstanding balance due and payable as of the Effective Date of this Agreement under the Second Note (as set forth above) and $1,111,151.74 is outstanding, due and payable as of the Effective Date of this Agreement under the Fourth Note are accurate and not in dispute; all payments shall be applied first to the Second Note until paid in full and then to the Fourth Note. Nothing herein shall constitute a waiver of any Existing Default, any future default, or any rights or remedies of the Lender, all of which are expressly reserved.

2. In consideration for the foregoing Forbearance, the Company will repay the outstanding balance of the Notes in the following installments (each an “Amended Installment Payment”) with payments, payable, at the option of the Company either in cash, or in Conversion Shares issued at the Default Conversion Price if such payment in Conversion Shares is approved by the Lender (the “Accepted Conversion Shares”), provided that such Accepted Conversion Shares are immediately salable by the Lender under Rule 144, as follows: (i) One Million Five Hundred Thousand Dollars ($1,500,000) upon the closing of the first funding of that certain financing transaction being conducted for the Company by RBW Capital Partners LLC, a division of Dawson James Securities, Inc. (the “RBW Financing”), to occur on or before May 7, 2026, to be applied to the outstanding balance of the Second Note, (ii) Two Million Five Hundred Thousand Dollars ($2,500,000) upon the second closing of the RBW Financing, to the applied to the outstanding balance of the Second Note, to occur upon the effectiveness of an S-1 Registration Statement, to be filed on or before May 13, 2026 and be effective on or before July 15, 2026, (iii) the remaining balance of the Second Note upon the earlier to occur of (a) closing of the transaction by and between the Company and Olenox Industries, Inc. that is the subject of a Term Sheet dated January 27, 2026 (the “Olenox Transaction”) or (b) receipt by the Company of any proceeds from an Advance under the Standby Equity Purchase Agreement (the SEPA”) that is a component of the RBW Financing, with the first Advance to be on or before August 15, 2026, in which fifty percent (50%) of the net proceeds of each Advance shall be paid directly to the Lender until the Second Note is paid in full; and (iv) the outstanding balance of the Fourth Note upon the earlier to occur of (a) closing of the Olenox Transaction, (b) fifty percent (50%) of the net proceeds from an Advance under the SEPA that is a component of the RBW Financing, with the first Advance to occur on or before August 15, 2026 and so long as the Second Note has been repaid in full, or (C) November 5, 2026 (the “Amended Repayment Terms”). The Company shall irrevocably direct RBW Capital Partners LLC, Dawson James Securities, Inc., and any

escrow agent, placement agent, transfer agent or other intermediary involved in the RBW Financing or SEPA advances to pay the Lender directly from the applicable proceeds in accordance with this Section and each of such third parties shall acknowledge in writing the payments to be made to the Lender pursuant to this Section 2. All payments received by the Lender shall be applied first to fees, costs and expenses, then to accrued interest, then to principal under the Second Note until the Second Note is paid in full, and thereafter in the same order to the Fourth Note. Except for the RBW Financing, the Olenox Transaction, and issuances expressly permitted herein, all proceeds of any debt or equity financing, issuance of Common Stock Equivalents, asset sale, strategic transaction, merger, acquisition financing or similar transaction shall be applied first to the Second Note until paid in full and thereafter to the Fourth Note until paid in full. In order to permit the Company to comply with Amended Repayment Terms, subject to the limitations hereinafter set forth, the Lender hereby consents to the Company entering into the RBW Financing, and all transactions contemplated thereunder, to the extent such consent is required under the Loan Agreement, this Agreement and all of the Transaction Documents delivered under the Loan Agreement: provided, that the Company shall not incur (1) more than $15,000,000 of Indebtedness under the RBW Financing, of which $6,000,000 shall be funded net of closing costs on or before May 7, 2026 and $6,000,000 shall be funded net of closing costs upon the effectiveness of an S-1 registration statement to be declared effective by the SEC on or before July 15, 2026, and (2) up to $100 million in SEPA Note payments from the two fundings under the RBW Financing and from exercise of the SEPA (collectively the “Permitted Financings”). For the avoidance of doubt, other than the foregoing Permitted Financings, no other Indebtedness for borrowed money, Common Stock, Common Stock Equivalents or other securities, including warrants or rights to purchase Equity Interests shall be permitted under this Agreement or the Transaction Documents without the prior written consent of the Lender.

3. Default Under This Agreement. In the event the Company fails to comply with the foregoing Amended Repayment Terms or otherwise defaults under this Agreement, then (i) the entire outstanding balance then due and payable under the Notes, including all principal, accrued interest, default interest, penalties, fees, costs, expenses and other amounts due, shall automatically increase to one hundred ten percent (110%) of the then Outstanding Amount of the Notes, (ii) such increased balance will begin accruing interest at nineteen percent (19%) per annum compounded daily and calculated on the basis of a 360-day year for actual days elapsed, (iii) the entire balance shall become immediately due and payable to the Lender in full without notice, demand, presentment or further action, (iv) the Forbearance provided herein shall automatically terminate, and (v) the Lender may exercise all of its rights and remedies under the Loan Agreement, the Notes, this Agreement and the other Transaction Documents. Any default under this Agreement shall constitute an Event of Default under the Loan Agreement, the Notes, and all other Transaction Documents. Upon the occurrence of any such default, this Agreement shall automatically terminate and be of no further force or effect, and the Loan Agreement and the Notes shall revert to the terms and conditions in effect immediately prior to the Effective Date of this Agreement, including all default interest, default conversion rights, premiums, penalties, fees, costs, expenses, and remedies, as if this Agreement had never been executed, without any further action required by the Lender. Additional Events of Default under this Agreement shall include, without limitation: (a) failure to make any payment required hereunder when due; (b) failure to direct RBW Capital Partners LLC, Dawson James Securities, Inc., any escrow agent, placement agent, transfer agent or other intermediary to pay the Lender directly as required herein; (c) failure of the first closing of the RBW Financing to occur on or before May 7, 2026; (d) failure to file the S-1 Registration Statement on or before May 13, 2026 or failure of such registration statement to become effective on or before July 15, 2026; (e) failure to complete the Olenox Transaction or a SEPA Advance sufficient to satisfy the payment obligations set forth herein on or before August 15, 2026; (f) the Company receiving any delisting notice or other notice of noncompliance from Nasdaq or any other trading market; (g) any default under the RBW Financing, any SEPA document, or any other loan, note, debenture, financing arrangement, lease, security agreement or material contract; (h) any issuance of debt, equity securities, Common Stock Equivalents or other securities except as expressly permitted herein; (i) any breach of any representation, warranty or covenant contained herein; or (j) any bankruptcy, insolvency, receivership, assignment for the benefit of creditors, liquidation, reorganization or similar proceeding involving the Company.

4. Existing Defaults. Vivakor acknowledges and confirms the occurrence of the Existing Defaults. Vivakor further acknowledges and agrees that, as of the Effective Date, (i) the outstanding balance of the Second Note is $6,815,805.71, (ii) the outstanding balance of the Fourth Note is $1,111,151.74, (iii) such amounts are accurate, valid, binding, due and owing, (iv) such amounts are not subject to dispute, defense, deduction, setoff, recoupment, counterclaim or avoidance of any kind, and (v) no payments have been made or received with respect to the Notes other than as expressly reflected in the balances set forth above.

5. Lender’s Representations and Warranties. Lender represents and warrants as follows:

a. It is not under any contractual or other restriction or other obligation which is inconsistent with this Agreement.

b. It has not assigned to any Person any right, claim or cause of action encompassed or arising from matters set forth in this Agreement.

c. It has had a full and fair opportunity to make inquiries about the terms and conditions of this Agreement, to discuss the same and all related matters with its own independent counsel, accountant and tax advisers; and this Agreement has been executed and delivered by it of its own free will and without promises, threats or the exertion of any duress.

d. This Agreement has been duly executed by Lender and, when delivered in accordance with the terms hereof and thereof, will constitute the valid and binding obligation of Lender enforceable against Lender in accordance with its terms, except: (i) as limited by general equitable principles and applicable bankruptcy, insolvency, reorganization, moratorium and other laws of general application affecting enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies and (iii) insofar as indemnification and contribution provisions may be limited by applicable law.

6. Lender represents and warrants that it is (i) an accredited investor familiar with the Company’s operations, (ii) aware of the risks inherent with an investment in the Company’s Common Stock, (iii) acquiring the Company’s Common Stock as an investment for its own account and not as a nominee or agent, and (iv) aware that the Company’s Common Stock is not registered under the Securities Act of 1933 (the “1933 Act”) and may not be sold, transferred, or otherwise disposed of without registration under the 1933 Act or an exemption therefrom under Rule 144, and that in the absence of an effective registration statement covering the Securities or an available exemption from registration under the 1933 Act, the Common Stock must be held indefinitely. Notwithstanding the foregoing and for the avoidance of doubt all Accepted Conversion Shares shall be fully registered for resale and may be immediately sold by the Lender.

7. Vivakor’s Representations, Warranties and Covenants. Vivakor hereby represents, warrants and covenants as follows:

a. It is not under any contractual or other restriction or other obligation which is inconsistent with this Agreement.

b. Except as disclosed in the Company’s filings with the Securities and Exchange Commission, there are no current or pending litigation matters.

c. It is not in default under any other loan agreement, except certain defaults that are not expected to have a material adverse effect on the Company.

d. It has not assigned to any Person any right, claim or cause of action encompassed or arising from matters set forth in this Agreement.

e. The execution and delivery of this Agreement and the consummation by it of the transactions contemplated hereby and thereby have been duly authorized by all necessary action on the part of the Company and no further action is required by the Company, its board of directors or the Company’s stockholders in connection therewith. This Agreement has been duly executed by the Company and, when delivered in accordance with the terms hereof, will constitute the valid and binding obligations of the Company, enforceable against the Company in accordance with its terms except: (i) as limited by general equitable principles and applicable bankruptcy, insolvency, reorganization, moratorium and other laws of general application affecting enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies and (iii) insofar as indemnification and contribution provisions may be limited by applicable law.

f. On or before June 30, 2026 the Company shall call a regular or special meeting of its stockholders (the “Stockholders Meeting”) pursuant to which, among other things, the Loan Agreement, this Agreement and all of the Transaction Documents delivered under the Loan Agreement, including the approval to issue more than 19.99% of the Company’s current outstanding common stock under the Notes (if not already obtained) upon conversion of the Notes into shares of the Company’s common stock, shall be approved by the holders of a majority of the outstanding voting securities of the Company (the “Shareholder Approval”). Unless previously approved by a majority of the Company’s shareholders, the Company may not issue shares to the Lender upon conversion of the Notes that exceeds 19.99% of the Company’s current outstanding common stock until it obtains Shareholder Approval. Notwithstanding the foregoing, the Company acknowledges the Shareholder Approval has been obtained with respect to the Second Note.

g. Except for the Permitted Financings, the Company shall not issue any promissory notes convertible into Common Stock, warrants exercisable for Common Stock, or new commitments to issue Common Stock (“Common Stock Equivalents”) unless and until the Notes, including the Default Amount and default interest and fees, shall have been paid in full. Except as contemplated by this Agreement, the Company may not issue any Common Stock, Common Stock Equivalents or incur any Indebtedness for borrowed money unless both the Second Note and the Fourth Note shall have been previously been paid in full or are paid in full out of the net proceeds of such financing.

h. The Company shall not take any action, or permit any affiliate, officer, director, employee, agent, lender, investor, transfer agent or other Person to take any action, that would impair, delay, subordinate, prime, avoid, challenge, contest or otherwise adversely affect the Lender’s rights, remedies, liens, security interests, conversion rights, Rule 144 resale rights, payment rights or priority under this Agreement, the Loan Agreement, the Notes or the other Transaction Documents. The Company shall execute and deliver such additional documents, instruments, notices, directions, UCC financing statements, control agreements and other agreements as the Lender may reasonably request to evidence, perfect, protect or enforce the Lender’s rights and remedies.

8. Binding. This Agreement shall inure to the benefit of the parties and shall be binding upon each of the parties and their assigns, successors, heirs, and representatives.

9. Authority. Each of the Parties represents and warrants that it has the authority to enter into this Agreement, that the person(s) signing this Agreement on its behalf is authorized to do so and that it has not assigned or otherwise transferred any interest in any claim which is the subject of this Agreement.

10. No Recitals. Each of the Parties agrees and understands that all of the terms of this Agreement are contractual and not merely recitals.

11. No Duress. Each of the Parties to this Agreement was represented by counsel and this Agreement was negotiated at arm’s length and should not be read against any party. Each of the Parties and their respective counsel acknowledge that they have carefully read and fully understand the provisions of this Agreement, that they have been given a reasonable period of time to consider the terms of this Agreement, and that they enter into this Agreement knowingly and voluntarily and not as a result of any pressure, coercion, or duress and thus no party shall attempt to invoke the rule of construction to the effect that ambiguities, if any, are to be resolved against the drafting party.

12. Severability. If any of the provisions of this Agreement is held by a court of competent jurisdiction to be invalid, void, or otherwise unenforceable, the remaining provisions shall nevertheless continue in full force and effect without being impaired or invalidated in any way.

13. Choice of Law and Venue; Waiver of Jury Trial; Confession of Judgement. This Agreement will be governed as to validity, interpretation, construction, effect and in all other respects by the internal laws of the State of Utah, without regard to conflicts of law principles. The Company and Lender each (i) agree that any legal suit, action or proceeding arising out of or relating to this Agreement shall be instituted exclusively in the Utah State Supreme Court, County of Salt Lake City, (ii) waives any objection to the venue of any such suit, action or proceeding, and the right to assert that such forum is an inconvenient forum, (iii) irrevocably consents to the jurisdiction of the Utah Supreme Court, County of Salt Lake City in any such suit, action or proceeding, and (iv) waive any right to arbitration with respect to any dispute arising out of or relating to this Agreement, the Loan Agreement, the Notes or the other Transaction Documents. Each of the Company and Lender further agrees to accept and acknowledge service of any and all process that may be served in any such suit, action or proceeding and agrees that service of process by certified mail or nationally recognized overnight courier to its address set forth for notices herein shall be deemed in every respect effective service of process. TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, EACH PARTY KNOWINGLY, VOLUNTARILY AND INTENTIONALLY WAIVES ANY RIGHT TO TRIAL BY JURY IN ANY ACTION, CLAIM, COUNTERCLAIM OR PROCEEDING ARISING OUT OF OR RELATING TO THIS AGREEMENT, THE LOAN AGREEMENT, THE NOTES OR THE OTHER TRANSACTION DOCUMENTS. To the fullest extent permitted by applicable law, the Company hereby authorizes the entry of judgment by confession in favor of the Lender for all amounts due under the Notes, this Agreement, the Loan Agreement and the other Transaction Documents following an Event of Default, together with interest, default interest, premiums, fees, costs, expenses and reasonable attorneys’ fees. The Company acknowledges that it has consulted with counsel regarding this confession of judgment provision or has had the opportunity to do so, and knowingly and voluntarily agrees to the same. The Company further reaffirms and grants to the Lender a continuing first-priority security interest in all collateral securing the Notes, including any collateral described in the Fourth Note, the Loan Agreement or any other Transaction Document, to secure all obligations owing under both the Second Note and the Fourth Note.

14. Entire, Final and Binding Agreement. Each of the Parties acknowledges and agrees that this Agreement is the final and binding Agreement between them concerning the matters addressed herein. This writing contains the entire Agreement of the Parties with respect to the subject matter hereof and, in entering into this Agreement, each of the Parties acknowledges that it has not relied on any promise, agreement, representation or statement, whether oral or written, that is not expressly set forth in this Agreement. Except as expressly modified by this Agreement during the Forbearance period, the Loan Agreement, the Notes and the other Transaction Documents remain in full force and effect. In the event of any inconsistency between this Agreement and any prior agreement between the Parties, the terms most favorable to the Lender shall control unless expressly waived by the Lender in writing.

15. Transaction Documents and Definitions. Except as amended pursuant to this Agreement, all of the other terms and conditions set forth in the Transaction Documents shall remain in full force and effect and are incorporated herein by this reference. Unless otherwise defined in this Agreement, all capitalized terms when used herein shall have the same meaning as such terms are defined in the Transaction Documents.

16. Amendments or Waivers. No change to or modification of this Agreement shall be valid or binding unless it is in writing and signed by the Parties.

17. Counterparts. This Agreement may be signed in counterparts and, if so signed, this Agreement shall have the same force and effect as if signed at the same time. A facsimile, docusign or PDF signature shall be deemed to be an original signature for all purposes.

18. Notices. Any and all notices or other communications or deliveries required or permitted to be provided hereunder shall be in writing and shall be deemed given and effective on the earliest of: (a) the date of transmission, if such notice or communication is delivered via e-mail at the email addresses set forth on the signature pages attached hereto at or prior to 5:30 p.m. (New York City time) on a business day, (b) the next business day after the date of e-mail, if such notice or communication is delivered via email at the email address set forth on the signature pages attached hereto on a day that is not a business day or later than 5:30 p.m. (New York City time) on any business day, (c) the second (2nd) business day following the date of mailing, if sent by U.S. nationally recognized overnight courier service or (d) upon actual receipt by the party to whom such notice is required to be given. The address for such notices and communications shall be as set forth above.

Signature page follows

IN WITNESS WHEREOF, expressly intending to be legally bound, the Parties through their duly authorized agents, have executed this Agreement as of the date set forth above, effective as of the Effective Date.