On the solutions of a nonlinear fractional integro-differential equation of pantograph type
This article considers a fractional integro-differential equation on \([0,T]\) of the form \[ D^\alpha u(t) = f(t,u(t),u(pt)) + \int_0^{qt} g_1(t,s,u(s)) \,ds + \int_0^t g_2(t,s,u(s)) \,dx, \] where \(0 < \alpha, p, q < 1\), \(D^\alpha\) is the Caputo fractional derivative, and \(f\), \(g_1\), \(g_2\) are continuous. The authors first prove the existence and uniqueness of the solution, and then present a numerical method based on sinc functions. Some numerical examples are given.
fractional integro-differential equation
scientific article; zbMATH DE number 6804290
scientific article