Browsing by Author "Zayed, Ahmed I."

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Fractal Calculus of Variations: A New Framework
(Springer Basel Ag, 2025) Golmankhaneh, Alireza Khalili; Tunc, Cemil; Depollier, Claude; Zayed, Ahmed I.
In this paper, we give a short summary of fractal calculus. We introduce the concept of fractal variation of calculus and derive the general form of the fractal Euler equation, along with an alternate form. We explore applications of the fractal Euler equation, including the optical fractal path near the event horizon of a black hole and determining the shortest distance in fractal space. Examples and illustrative plots are provided to demonstrate the detailed behavior of these equations and their practical implications.
Solving Fractal Differential Equation Via Numerical Methods
(Springer Heidelberg, 2025) Golmankhaneh, Alireza Khalili; Zayed, Ahmed I.; Myrzakulov, Ratbay
In this paper, the fractal numerical methods for solving fractal differential equations are given such as the Fractal Euler's Method, the Fractal Heun Method, and the Fractal Runge-Kutta Method. The errors of the fractal numerical approximate solution of the fractal differential equation are presented and compared.