Document Type : Research Article
Authors
Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran
10.30473/coam.2026.76466.1358
Abstract
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.
Highlights
- Introduces two-dimensional fractional-order Fibonacci wavelets (FOFWs) for solving variable-order fractional integro-differential equations (VOFIDEs).
- Derives accurate variable-order fractional integral/derivative matrices, transforming VOFIDEs into algebraic systems via collocation.
- Proves convergence via theorems, ensuring reliability under appropriate conditions.
- Numerical examples confirm high accuracy, stability, and efficiency, with error reduction via increased resolution parameters.
- Flexible framework extensible to nonlinear/higher-dimensional fractional models.
Keywords
- Fractional-order Fibonacci wavelets
- Fibonacci polynomial
- Taylor expansion
- Collocation method
- Operational matrices
Main Subjects
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