Fractional calculus and Sinc methods

Abstract

Abstract Fractional integrals, fractional derivatives, fractional integral equations, and fractional differential equations are numerically solved by Sinc methods. Sinc methods are able to deal with singularities of the weakly singular integral equations of Riemann-Liouville and Caputo type. The convergence of the numerical method is numerically examined and shows exponential behavior. Different examples are used to demonstrate the effective derivation of numerical solutions for different types of fractional differential and integral equations, linear and non-linear ones. Equations of mixed ordinary and fractional derivatives, integro-differential equations are solved using Sinc methods. We demonstrate that the numerical calculation needed in fractional calculus can be gained with high accuracy using Sinc methods.