Extended truncated exponential method for solving tempered fractional variational problems

In this paper, we propose a novel method, that is, extended truncated exponential (ETE) method for solving tempered fractional variational problems (TFVPs) with integral constraints. The method leverages the extended truncated exponential function (ETEF) and the tempered Caputo fractional derivative (TCFD) to transform TFVPs into solvable algebraic systems. We derive the operational matrix of derivatives for the ETEF and apply it to approximate the solutions of TFVPs efficiently. The method demonstrates superior performance in terms of computational efficiency and accuracy compared to existing approaches. Several numerical examples validate the effectiveness of our method.