Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations

• Singular fractional Volterra integro-differential equations.
• In this paper it is given a method for solving singular fractional volterra integro-differential equations.
• This method is focussed on a special family of wavelets (Chebyshev).
• Chebyshev wavelets are some special wavelets having both the many advantages of wavelets and the Chebyshev polynomials.
• Operational matrix: the fractional derivatives when applied to some polynomials enable to define some operational matrices.
• These matrices will be explicitly computed.
• This method is applied to some examples and the error is explicitly computed.

This paper presents a computational method for solving a class of system of nonlinear singular fractional Volterra integro-differential equations. First, existences of a unique solution for under studying problem is proved. Then, shifted Chebyshev polynomials and their properties are employed to derive a general procedure for forming the operational matrix of fractional derivative for Chebyshev wavelets. The application of this operational matrix for solving mentioned problem is explained. In the next step, the error analysis of the proposed method is investigated. Finally, some examples are included for demonstrating the efficiency of the proposed method.