Work

Analyzing Uniqueness of Solutions in Nonlinear Fractional Differential Equations with Discontinuities Using Lebesgue Spaces

Year: 2024

Type: article

Abstract: We explore the existence and uniqueness of solutions to nonlinear fractional differential equations (FDEs), defined in the sense of RL-fractional derivatives of order η∈(1,2). 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.

Source: Axioms

DOI: 10.3390/axioms14010026

Authors: Farva Hafeez, Mdi Begum Jeelani, Nouf Abdulrahman Alqahtani

Institutions: University of Lahore, Imam Mohammad ibn Saud Islamic University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

OpenAlex ID: W4405942853

FWCI:

Cites: 22

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Related to: 10