Analytical and Approximate Solution for Solving the Vibration String Equation with a Fractional Derivative

Temirkhan S. Aleroev and Asmaa M. Elsayed
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Temirkhan S. Aleroev: Department of Applied Math, Moscow State University of Civil Engineering, 129337 Moscow, Russia
Asmaa M. Elsayed: Department of Applied Math, Moscow State University of Civil Engineering, 129337 Moscow, Russia

Mathematics, 2020, vol. 8, issue 7, 1-9

Abstract: This paper is proposed for solving a partial differential equation of second order with a fractional derivative with respect to time (the vibration string equation), where the fractional derivative order is in the range from zero to two. We propose a numerical solution that is based on the Laplace transform method with the homotopy perturbation method. The method of the separation of variables (the Fourier method) is constructed for the analytic solution. The derived solutions are represented by Mittag–LefLeffler type functions. Orthogonality and convergence of the solution are discussed. Finally, we present an example to illustrate the methods.

Keywords: laplace transform; homotopy perturbation method; fractional PDEs; Mittag–Leffler type functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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