On General Form of Fractional Delay Integro-Differential Equations

Abstract

In this paper, a numerical solution of general form of fractional delay integro-differential equation (GFDIDE) is presented using spectral collocation method. The Chebyshev polynomials of the second kind are used as a basis function with the collocation scheme. The proposed equation represents a general form of intgro-differential equation with delayed argument, which has multi-terms of integer and fractional order derivatives for delayed or non-delayed terms. The operation matrices for all terms of GFDIDE are introduced according to fractional calculus. The reliability and efficiency of the proposed method are demonstrated by some numerical examples.

Keywords

• chebyshev second kind collocation method
• general fractional order delay integro-differential equations
• caputo fractional derivatives