In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a 2α-order fractal differential equation with constant coefficients across different scenarios. We propose a uniqueness theorem for 2α-order fractal linear differential equations. We define the solution space as a vector space with non-integer orders. We establish precise conditions for 2α-order fractal linear differential equations and derive the corresponding fractal adjoint differential equation.
Khalili Golmankhaneh, A., Bongiorno, D. (2024). Fractal Differential Equations of 2α-Order. AXIOMS, 13(11), 1-20 [10.3390/axioms13110786].
Fractal Differential Equations of 2α-Order
Bongiorno, Donatella
2024-11-14
Abstract
In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a 2α-order fractal differential equation with constant coefficients across different scenarios. We propose a uniqueness theorem for 2α-order fractal linear differential equations. We define the solution space as a vector space with non-integer orders. We establish precise conditions for 2α-order fractal linear differential equations and derive the corresponding fractal adjoint differential equation.
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