Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 Articles in Press 2026 04 21 Solving Variable-Order Fractional Integro-Differential Equations Using the Two-Dimensional Fractional-Order Fibonacci Wavelets Operational Matrix 12846 10.30473/coam.2026.76466.1358 EN Shiva Karimi Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran 0000-0002-2128-6250 Elyas Shivanian Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran Zahra Barikbin Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran Journal Article 2025 11 12 This paper presents a novel numerical method for solving variable-order fractional integro-differential equations using two-dimensional fractional-order Fibonacci wavelets. The proposed approach employs fractional-order Fibonacci wavelets together with their associated integral and derivative operational matrices. First, new integral and derivative operational matrices are derived. These matrices, which exhibit improved accuracy in the numerical examples reported herein, are then employed to transform the governing equation into a system of algebraic equations. The collocation method is subsequently applied to solve this system and determine the unknown coefficients. Finally, error analysis, convergence results based on relevant theorems, and numerical examples are provided to demonstrate the accuracy, reliability, and efficiency of the proposed method. https://mathco.journals.pnu.ac.ir/article_12846_2408c41840d44f8254a11e9b094aa477.pdf