Analyzing Uniqueness of Solutions in Nonlinear Fractional Differential Equations with Discontinuities Using Lebesgue Spaces - Farva Hafeez; Mdi Begum Jeelani; Nouf Abdulrahman Alqahtani (Axioms)
We explore the existence and uniqueness of solutions to nonlinear fractional differential equations (FDEs), defined in the sense of RL-fractional derivatives of order <semantics>η∈(1,2)</semantics>. The nonlinear term is assumed to have a discontinuity at zero. By employing techniques from Lebesgue spaces, including Holder’s inequality, we establish uniqueness theorems for this problem, analogous to Nagumo, Krasnoselskii–Krein, and Osgood-type results. These findings provide a fundamental framework for understanding the properties of solutions to nonlinear FDEs with discontinuous nonlinearities.