In this paper, the exact solutions of certain non-linear differential equations defined on a fractal subset of the real line are presented. Particular attention is paid to the Riccati-type fractal differential equation, for which a connection with the Schrödinger equation is also provided. To further substantiate the theoretical findings, numerical validations are included, comparing the exact analytical solutions with results obtained through a generalized Fractal Euler Method.
Bongiorno, D., Khalili Golmankhaneh, A. (2026). Exact solutions for classes of nonlinear differential equations on fractal supports. NONLINEAR SCIENCE, 7(1), 1-17 [10.1016/j.nls.2026.100128].
Exact solutions for classes of nonlinear differential equations on fractal supports
Donatella Bongiorno
Primo
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2026-07-01
Abstract
In this paper, the exact solutions of certain non-linear differential equations defined on a fractal subset of the real line are presented. Particular attention is paid to the Riccati-type fractal differential equation, for which a connection with the Schrödinger equation is also provided. To further substantiate the theoretical findings, numerical validations are included, comparing the exact analytical solutions with results obtained through a generalized Fractal Euler Method.
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