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

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Akrami Mohammad Hossein; Poya Abbas; Zirak Mohammad Ali

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Journal Paper

Paper Information

Journal: Journal of Mahani Mathematical Research Year:2024 | Volume:13 | Issue:2 Page(s): 571-593

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Title

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

Author(s)

Akrami Mohammad Hossein | Poya Abbas | Zirak Mohammad Ali | Issue Writer Certificate

Keywords

Tempered fractional derivative

‎Mittag-Leffler function‎

‎fractional diffusion equation‎

Abstract

‎ 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.

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