New technique for solving system of variable-order fractional partial integro differential equations

In this manuscript a new numerical method is introduced for solving system of variable-order time fractional Volterra–Fredholm partial integro-differential equations involved with weakly singular kernels. The fractional derivative is described in the Caputo sense. The main idea is to use first Chebyshev wavelets and operational matrix of fractional order. By using the operational matrix and the effective collocation method, the variable-order time fractional partial integro differential equation is discretized into a system of algebraic equation. Numerical examples illustrate the effectiveness, applicability and accuracy of the proposed method.