The generalized variational iteration method to solve the fractal partial differential equations

Subject Areas : Numeric Analyze

Homa  Afraz ¹ (department mathematic, Payame Noor University: Tehran, IR)
Alireza  Khalili Golmankhaneh ² (Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran)

Received: 2022-09-24 Accepted : 2022-12-13 Published : 2023-08-01

Keywords: معادلات دیفرانسیل مشتقات جزئی فرکتال, فرکتال, روش تکرار تغییراتی تعمیم یافته, حسابان فرکتال,

Abstract :

Fractional calculus is a branch of classical mathematics, which deals with the generalization of fractional order derivative and integral operator. Recently, a great deal of research has been carried out on the fractional calculus to study the phenomena associated with fractal structures and processes. Fractals have a fractional dimension and occur naturally in non-linear and imbalanced phenomena in various forms and contexts. In recent years, various types of derivatives and fractional and fractal calculus have been proposed by many scientists and have been extensively utilized. Measurements are localized in physical processes, and local fractional calculus is a useful tool for solving some type of physical and engineering problems. Gangal studied the local fractional calculus and got the relation between it and the fractals. Using the local fractional calculus and fractal properties, he defined the fractal-alpha calculus on a subset of the real line, which is a simple calculs, useful, structural and algorithmic. In this study, we first describe the fractal-F alpha calculus. Next, we propose The generalized variational iteration method based on the fractal calculus. To show the efficiency of fractal calculus and the new method, we solve several fractal partial differential equations with this method and show that this method is better, easier and more suitable than the two other methods mention the above.

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