Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero

Year 2020, Volume: 49 Issue: 5, 1718 - 1725, 06.10.2020

Uğur Sert , Müfit Şan

https://doi.org/10.15672/hujms.512563

Cited By: 5

Abstract

In this article, we consider an initial value problem for a nonlinear differential equation with Riemann-Liouville fractional derivative. By proposing a new approach, we prove local existence and uniqueness of the solution when the nonlinear function on the right hand side of the equation under consideration is continuous on $(0,T]\times\mathbb{R}.$

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Keywords

Fractional differential equations, mean value theorem, Nagumo-type uniqueness, Peano-type existence theorem

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