Document Type : Research Paper

Authors

• Isa Zamanpour
• Reza Ezzati

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

• Singular integral equation
• Two-dimensional Fibonacci polynomials
• Operational matrix
• Fractional calculus