Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

Abstract In this article we propose a hybrid method based on local meshless and the Laplace transform for approximating solution of linear one dimensional partial differential equations in sense Caputo–Fabrizio fractional derivative. our numerical scheme is used to avoid time stepping procedure, produce sparse differentiation matrices ill conditioning issues resulting global methods. Our comprises three steps. first step given equation an equivalent independent equation. Secondly reduced solved via method. Finally, original obtained inverse by representing it as contour integral complex left half plane. The then approximated using trapezoidal rule. stability convergence are discussed. efficiency, efficacy, accuracy proposed assessed four different problems. Numerical approximations these problems validated against exact solutions. results show that can solve such types efficiently.