An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions

Mamta Kapoor, Nehad Ali Shah, Salman Saleem and Wajaree Weera
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Mamta Kapoor: Department of Mathematics, Lovely Professional University, Phagwara 144411, Punjab, India
Nehad Ali Shah: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
Salman Saleem: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
Wajaree Weera: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Mathematics, 2022, vol. 10, issue 12, 1-26

Abstract: In the present research paper, an iterative approach named the iterative Shehu transform method is implemented to solve time-fractional hyperbolic telegraph equations in one, two, and three dimensions, respectively. These equations are the prominent ones in the field of physics and in some other significant problems. The efficacy and authenticity of the proposed method are tested using a comparison of approximated and exact results in graphical form. Both 2D and 3D plots are provided to affirm the compatibility of approximated-exact results. The iterative Shehu transform method is a reliable and efficient tool to provide approximated and exact results to a vast class of ODEs, PDEs, and fractional PDEs in a simplified way, without any discretization or linearization, and is free of errors. A convergence analysis is also provided in this research.

Keywords: fractional calculus; Shehu transform; iterative method; 1D; 2D; 3D fractional hyperbolic telegraph equation; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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