Nonlocal problem for multi-parametric integral-differential equation

Abstract

This paper investigates a nonlocal boundary value problem for a multi-parametric integral-differential equation involving the Caputo-Prabhakar type operator in a bounded rectangular domain. The nonlocal conditions are given as partial integral expressions of the unknown function with continuous kernels. Using a known representation of the solution to the corresponding Goursat problem in terms of bivariate and trivariate Mittag-Leffler-type functions, the problem is reduced to a system of Volterra integral equations of the second kind for boundary traces. Based on this reduction, sufficient conditions ensuring existence and uniqueness of the solution are established. An explicit representation of the solution is also obtained via the solution of the derived integral system.