A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity

Mufit San; Seyma Ramazan; Mufit San; Seyma Ramazan

doi:10.3934/era.2024141

Electronic Research Archive

2024, Volume 32, Issue 5: 3092-3112. doi: 10.3934/era.2024141

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Research article

A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity

Mufit San ^,,
Seyma Ramazan

Department of Mathematics, Cankiri Karatekin University, Cankiri, Turkey

Received: 26 February 2024 Revised: 14 April 2024 Accepted: 17 April 2024 Published: 24 April 2024

In this paper, we study an initial value problem with a weakly singular nonlinear fractional differential equation of higher order. First, we establish the existence of global solutions to the problem within the appropriate function space. We then introduce a generalized Riemann-Liouville mean value theorem. Using this theorem, we prove the Nagumo-type uniqueness theorem for the stated problem. Moreover, we give two examples to illustrate the applicability of the existence and uniqueness theorems.
- weakly singular integral equation,
- fractional differential equation,
- initial value problem,
- global existence
Citation: Mufit San, Seyma Ramazan. A study for a higher order Riemann-Liouville fractional differential equation with weakly singularity[J]. Electronic Research Archive, 2024, 32(5): 3092-3112. doi: 10.3934/era.2024141

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Abstract

In this paper, we study an initial value problem with a weakly singular nonlinear fractional differential equation of higher order. First, we establish the existence of global solutions to the problem within the appropriate function space. We then introduce a generalized Riemann-Liouville mean value theorem. Using this theorem, we prove the Nagumo-type uniqueness theorem for the stated problem. Moreover, we give two examples to illustrate the applicability of the existence and uniqueness theorems.

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