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

10.22075/ijnaa.2023.29867.4281

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


Articles in Press, Corrected Proof
Available Online from 19 March 2023
  • Receive Date: 10 January 2023
  • Revise Date: 01 March 2023
  • Accept Date: 02 March 2023
  • First Publish Date: 19 March 2023