Numerical Technique Based on Operational Matrices of Fractional Integration Using ψ $$ \psi $$ -Shifted Chebyshev Polynomials

Abstract

In this paper, we present a numerical scheme based on a modified form of shifted Chebyshev polynomials to find the numerical solution of a class of fractional differential equations. For this purpose, we work out operational matrices of fractional integration of $\psi$-shifted Chebyshev polynomials obtained from shifted Chebyshev polynomials. Finally, the solution to the problem under consideration is obtained by solving a system of algebraic equations that results from the use of operational matrices of integration. The analysis of integer and non-integer order differential equations is presented to show the convergence of the solution of fractional order differential equation to the corresponding solution of the integer order differential equation. At the end, we present some linear and non-linear examples to validate the theoretical analysis. Non-linear examples are solved using Quasilinearization and proposed numerical technique.