OPERATIONAL MATRICES TO SOLVE NONLINEAR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS OF MULTI-ARBITRARY ORDER

Abstract

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

Keywords

• Fractional order of Chebyshev functions,Operational matrix; Volterra-Fredholm integro- differential equations; Tau-Collocation method

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