A study on fractional Klein Gordon equation with non-local and non-singular kernel

Abstract

This manuscript focus primarily on the numerical treatment of time fractional Klein Gordon (KG) equation using the Atangana-Baleanu fractional derivative which combines both nonlocal and nonsingular properties. A noble numerical technique based on Adams-Bashforth method is adopted for the numerical approximation of the KG equation. A detailed mathematical analysis showing the existence and uniqueness of the solutions is presented using the Picard-Lindelof theorem and the theory of fixed point. Stability analysis of the newly obtained numerical scheme for Klein Gordon equation is examined via the Ulam Hyers stability approach. The applicability of the numerical method is justified via some numerical experiments obtained for different instances of fractional order alpha. (C) 2019 Elsevier Ltd. All rights reserved.