Solving fractional two-dimensional nonlinear weakly singular partial integro-differential equation by using Fibonacci polynomials

	Solving fractional two-dimensional nonlinear weakly singular partial integro-differential equation by using Fibonacci polynomials
International Journal of Nonlinear Analysis and Applications
مقاله 2، دوره 14، شماره 11، بهمن 2023، صفحه 11-24 اصل مقاله (530.61 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29867.4281
نویسندگان
Isa Zamanpour؛ Reza Ezzati^*
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
چکیده
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.
کلیدواژه‌ها
Singular integral equation؛ Two-dimensional Fibonacci polynomials؛ Operational matrix؛ Fractional calculus
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