Solving the fractional order integro-differential equations using fractional Jacobi functions

Authors
Zahra Delkhoush
Maryam Arabameri
University of Sistan and Baluchestan
Abstract
In this paper, we are intend to present a numerical algorithm for computing approximate solution of linear and nonlinear Fredholm, Volterra and Fredholm-Volterra integro-differential equations. The approximated solution is written in terms of fractional Jacobi polynomials. In this way, firstly we define Riemann-Liouville fractional operational matrix of fractional order Jacobi polynomials, then by using this matrix and the least squares method the solution of equation reduce to a system of algebraic equations which is solved through the Newton’s iterative method. In the next step we analyze convergence of the solution, and then to confirm the theoretical issue we examine some numerical examples. The results indicate the accuracy and efficiency of the method. The excellence of this method is its generality, which includes the fractional order Legendre and Chebyshev polynomials. Also it is also easy to use for linear and nonlinear integro-differential equations and provides good results.
Keywords
Operational matrix
Least squares method
Orthogonal polynomials
Best approximation
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