@article{article_512563, title={Some analysis on a fractional differential equation with a right-hand side which has a discontinuity at zero}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={49}, pages={1718–1725}, year={2020}, DOI={10.15672/hujms.512563}, author={Sert, Uğur and Şan, Müfit}, keywords={Fractional differential equations, mean value theorem, Nagumo-type uniqueness, Peano-type existence theorem}, abstract={<p>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 $(0,T]\times\mathbb{R}.$ </p> <p> <font color="#ffffff">*********************************************************************************************************************************************** </font> </p> <p> <font color="#ffffff">*********************************************************************************************************************************************** <br /> </font> </p>}, number={5}, publisher={Hacettepe University}