A numerical approach for solving the Fractal ordinary differential equations

Pashmakian, Nooshin; Farajzadeh, Ali; Parandin, Nordin; Karamikabir, Nasrin

doi:10.22034/cmde.2023.55868.2331

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	A numerical approach for solving the Fractal ordinary differential equations
Computational Methods for Differential Equations
مقاله 11، دوره 12، شماره 4، دی 2024، صفحه 780-790 اصل مقاله (1.76 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.55868.2331
نویسندگان
Nooshin Pashmakian¹؛ Ali Farajzadeh^* ²؛ Nordin Parandin³؛ Nasrin Karamikabir¹
¹Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
²Department of Mathematics, Razi University, Kermanshah, Iran.
³Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.
چکیده
In this paper, fractal differential equations are solved numerically. Here, the typical fractal equation is considered as follows: $$\frac{du(t)}{dt^{\alpha}}=f\left\{ t,u(t)\right\},~~~\alpha>0,$$ $f$ can be a nonlinear function and the main goal is to get $u(t)$. The continuous and discrete modes of this method have differences, so the subject must be carefully studied. How to solve fractal equations in their discrete form will be another goal of this research and also its generalization to higher dimensions than other aspects of this research.
کلیدواژه‌ها
Fractal Differential Equations؛ Taylor series؛ Continuous؛ Discrete points

مراجع
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A numerical approach for solving the Fractal ordinary differential equations