Novel technique to investigate the convergence analysis of the tempered fractional natural transform method applied to diffusion equations

Abstract

In this research work, we present proof of the existence and uniqueness of solution for a novel method called tempered fractional natural transforms (TFNT) and give error estimates. This efficient method is applied to models, such as the time-space tempered fractional convection-diffusion equation (FCDE) and tempered fractional Black-Scholes equation (FBSE). We obtain exact solutions for these models using our methodology, which is very important for knowing the wave behavior in ocean engineering models and for the studies related to marine science and engineering. Finding exact solutions to tempered fractional differential equations (TFDEs) is far from trivial. Therefore, the proposed method is an excellent addition to the myriad of techniques for solving TFDE problems.