Higher Order Fractal Differential Equations

Alireza Khalili Golmankhaneh; Claude Depollier; Diana Pham

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arXiv · 2404.00452

Higher Order Fractal Differential Equations

Alireza Khalili Golmankhaneh·Claude Depollier·Diana Pham

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Abstract

This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-order. Solutions for these equations with constant coefficients are obtained through the method of variation of parameters and the method of undetermined coefficients. The solution space for higher $\alpha$-order linear fractal differential equations is defined, showcasing its non-integer dimensionality. The solutions to $\alpha$-order linear fractal differential equations are graphically depicted to illustrate their non-differentiability. Additionally, equations of motion governing the behavior of two masses in fractal time are proposed and solved.

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BibTeX RIS

Alireza Khalili Golmankhaneh, Claude Depollier, Diana Pham. 2024-03-30. Higher Order Fractal Differential Equations. https://arxiv.org/abs/2404.00452

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