A new method for solving fractional partial differential equations. (English) Zbl 1451.35256

Özkan, Ozan; Kurt, Ali

J. Anal. 28, No. 2, 489-502 (2020).

Several books and papers deal with Integrals and differentials of arbitrary order e.g. [St. G. Samko et al., Fractional integrals and derivatives: theory and applications. Transl. from the Russian. New York, NY: Gordon and Breach (1993; Zbl 0818.26003)]. In this paper the authors consider, so called “Laplace differential transform method”. This method is a combination of the Laplace transform and “Differential transform method” [J. K. Zhou, Differential transformation and its application for electrical circuits. Wuhan: Huazhong University Press (1986); C.-K. Chen and S.-H. Ho, Appl. Math. Comput. 79, No. 2–3, 173–188 (1996; Zbl 0879.34077)]. Numerical solutions of fractional differential equations have been considered by several authors [R. Scherer et al., Comput. Math. Appl. 62, No. 3, 902–917 (2011; Zbl 1228.65121)]. The authors use Laplace Differential Transform Method to obtain approximate solutions of some fractional partial differential equations.

Reviewer: S. L. Kalla (Ballwin)

MSC:

35R11	Fractional partial differential equations
44A10	Laplace transform
35A22	Transform methods (e.g., integral transforms) applied to PDEs
35C10	Series solutions to PDEs

Keywords:

Laplace transform; fractional; partial differential equations; series solutions

Citations:

Zbl 0818.26003; Zbl 0879.34077; Zbl 1228.65121

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