The existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown function

Aleksic, SuzanaCabada Fernández, AlbertoDimitrijevic, SladjanaTomovic Mladenovic, Tatjana V.2025-02-182025-02-1820230354-5180https://hdl.handle.net/10347/39699In this paper, we consider the existence of solutions of the nonlinear fractional differential equation boundary-value problem Dα* u(t) = f (t, u(t), u′(t), CDβu(t)), 0 < t < 1, 1 < α < 2, 0 < β ≤ 1, u(0) = A, u(1) = Bu(η), where 0 < η < 1, A ≥ 0, Bη > 1, Dα* is the modified Caputo fractional derivative of order α, CDβ is the Caputo fractional derivative of order β, and f is a function in C([0, 1] × R × R × R). Existence results for a solution are obtained. Two examples are presented to illustrate the results.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Fractional Differential EquationsGreen’s FunctionsBoundary Value Problem120215 Ecuaciones integralesThe existence of a solution for nonlinear fractional differential equations where nonlinear term depends on the fractional and first order derivative of an unknown functionjournal articlehttps://doi.org/10.2298/FIL2312871A2406-0933open access