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

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San M., SERT U.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.5, pp.1718-1725, 2020 (SCI-Expanded, Scopus, TRDizin)

• Publication Type: Article / Article
• Volume: 49 Issue: 5
• Publication Date: 2020
• Doi Number: 10.15672/hujms.512563
• Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
• Page Numbers: pp.1718-1725
• Open Archive Collection: AVESIS Open Access Collection
• Hacettepe University Affiliated: Yes

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] x R.