On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions

Abstract

Abstract In this paper, the semi-group method is used to discuss the existence and uniqueness of solutions for fractional and partial integro differential equations (F-PIDEs) of heat type in Banach space E. In addition, the stability of the solutions for F-PIDEs are discussed. Moreover, the Adomian decomposition method (ADM) is used to obtain the solutions numerically. Finally, numerical results of each case are obtained, and the difference of results between the fractional partial integro differential equation and partial integro differential equation are explained. Furthermore, the error is computed in each case.