International Journal of Nonlinear Analysis and Applications
Solving fractional two-dimensional nonlinear weakly singular partial integro-differential equation by using Fibonacci polynomials
Document Type : Research Paper
Authors
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Abstract
The main aim of the present study is to expand the operational matrix method for solving the fractional two-dimensional nonlinear weakly singular partial integro-differential equations. To do this, firstly, we use and present the operational matrix of fractional integration of two-dimensional Fibonacci polynomials. Then, by using the obtained operational matrices to approximate the fractional derivative of the solution of the considered equation, we convert the original problem to a nonlinear system of equations. Also, we present the error analysis of the proposed method by a theorem. Finally, we present and solve some numerical examples to illustrate the proposed method.
Keywords
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Volume 14, Issue 11
November 2023Pages 11-24
- Receive Date: 10 January 2023
- Revise Date: 27 February 2023
- Accept Date: 02 March 2023