Second $\alpha$-Order Fractal Differential Equations

Alireza Khalili Golmankhaneh; Donatella Bongiorno

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arXiv · 2404.00428

Second $\alpha$-Order Fractal Differential Equations

Alireza Khalili Golmankhaneh·Donatella Bongiorno

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Abstract

In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a second $\alpha$-order fractal differential equation with constant coefficients across different scenarios. We propose a uniqueness theorem for second $\alpha$-order fractal linear differential equations. We define the solution space as a vector space with non-integer orders. We establish precise conditions for second $\alpha$-order fractal linear differential equations and derive the corresponding fractal adjoint differential equation.

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Alireza Khalili Golmankhaneh, Donatella Bongiorno. 2024-03-30. Second $\alpha$-Order Fractal Differential Equations. https://arxiv.org/abs/2404.00428

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