Computational analysis of local fractional partial differential equations in realm of fractal calculus. (February 2023)

• Record Type: Journal Article
• Authors: Kumar, Devendra; Dubey, Ved Prakash; Dubey, Sarvesh; Singh, Jagdev; Alshehri, Ahmed Mohammed
• Is Part Of: Chaos, solitons and fractals. Volume 167(2023)
• Publication Date: 2023-02
• Subjects: Local fractional partial differential equation -- Local fractional derivative -- Local fractional Sumudu transform -- Cantor set; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.113009
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this paper, a hybrid local fractional technique is applied to some local fractional partial differential equations. Partial differential equations modeled with local fractional derivatives easily capture the behavior of fractal models. The present technique is a copulation of local fractional homotopy method and local fractional integral transform. Four examples are provided to show the efficiency of an implemented method. Furthermore, computer simulations have also been performed for all the four examples of local fractional partial differential equations in a fractal domain. The working procedure depicts that the applied technique is very useful to acquire solutions for given local fractional partial differential equations in an efficient way. Moreover, the obtained solutions are also in good agreement with solutions computed by other methods. Highlights: A hybrid local fractional technique is applied to some local fractional partial differential equations (LFPDEs) The present technique is a mixture of local fractional homotopy method and local fractional integral transform. Four examples are provided to show the efficiency of the implemented method. Computer simulations have also been performed for all the four examples of LFPDEs in a fractal domain. The results depicts that the applied technique is very useful to acquire solutions for LFPDEs.