Numerical Solution of the Nonlinear Integro- Differential Equations of Multi-Arbitrary Order

Mehdi Delkhosh, Kourosh Parand

Abstract

Fractional calculus has been used for modelling many of physical and engineering processes, that many of them are described by nonlinear Fredholm integro- differential equations of multi-arbitrary (integer or fractional) order. Therefore, an efficient and suitable method for the solution of them is too important. In this paper, the generalized fractional order of the Chebyshev functions (GFCFs) based on the classical Chebyshev polynomials of the first kind have been expressed that can be used to obtain the solution of the nonlinear Fredholm integro- differential equations of multi-arbitrary order. Also, the operational matrices of fractional derivative, the product, and the dual for the GFCFs, that they convert the differential equations to a system of algebraic equations, have been constructed. Some examples are included to demonstrate the validity and applicability of the technique.