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

#### Uğur SERT [1] , Müfit ŞAN [2]

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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Fractional differential equations, mean value theorem, Nagumo-type uniqueness, Peano-type existence theorem
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Primary Language en Mathematics Mathematics Orcid: 0000-0003-4783-6983Author: Uğur SERT (Primary Author)Institution: Hacettepe UniversityCountry: Turkey Orcid: 0000-0001-6852-1919Author: Müfit ŞAN Institution: CANKIRI KARATEKIN UNIVERSITYCountry: Turkey Publication Date : October 6, 2020
 Bibtex @research article { hujms512563, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1718 - 1725}, doi = {10.15672/hujms.512563}, title = {Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero}, key = {cite}, author = {Sert, Uğur and Şan, Müfit} } APA Sert, U , Şan, M . (2020). Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1718-1725 . DOI: 10.15672/hujms.512563 MLA Sert, U , Şan, M . "Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1718-1725 Chicago Sert, U , Şan, M . "Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1718-1725 RIS TY - JOUR T1 - Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero AU - Uğur Sert , Müfit Şan Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.512563 DO - 10.15672/hujms.512563 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1718 EP - 1725 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.512563 UR - https://doi.org/10.15672/hujms.512563 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero %A Uğur Sert , Müfit Şan %T Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.512563 %U 10.15672/hujms.512563 ISNAD Sert, Uğur , Şan, Müfit . "Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 1718-1725 . https://doi.org/10.15672/hujms.512563 AMA Sert U , Şan M . Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1718-1725. Vancouver Sert U , Şan M . Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1718-1725.

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