Control Theory & Systems
Shiva Karimi; Elyas Shivanian; Zahra Barikbin
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 ...
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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.
