‎Exact analytical solution of tempered fractional heat-like (diffusion) equations by the modified variational iteration method

‎    This paper introduces a modified version of the Variational Iteration Method, incorporating $\mathbb{P}$-transformation. We propose a novel semi-analytical technique named the modified variational iteration method   for addressing fractional differential equations featuring tempered Liouville-Caputo derivatives. The modified variational iteration method emerges as a highly efficient and powerful mathematical tool, offering exact or approximate solutions for a diverse range of real-world problems in engineering and the natural sciences, specifically those expressed through differential equations. To assess its effectiveness and accuracy, we scrutinize the modified variational iteration method by applying it to three problems related to the heat-like multidimensional diffusion equation with a fractional time derivative in a tempered Liouville-Caputo form.