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Solving fractal differential equations via fractal Laplace transforms

Ali Karmina Kamal, Golmankhaneh Alireza Khalili, Yilmazer Resat, Abdullah Milad Ashqi

Journal of Applied Analysis

2022

Vol. 28, nr 2

237--250

The intention of this study is to investigate the fractal version of both one-term and three-term fractal differential equations. The fractal Laplace transform of the local derivative and the non-local fractal Caputo derivative is applied to investigate the given models. The analogues of both theWright function with its related definitions in fractal calculus and the convolution theorem in fractal calculus are proposed. All results in this paper have been obtained by applying certain tools such as the generalWright and Mittag-Leffler functions of three parameters and the convolution theorem in the sense of the fractal calculus. Moreover, a comparative analysis is conducted by solving the governing equation in the senses of the standard version and fractal calculus. It is obvious that when α = γ = β = 1, we obtain the same results as in the standard version.