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

Authors : Uğur SERT, Müfit ŞAN

Pages : 1718-1725

Doi:10.15672/hujms.512563

View : 11 | Download : 4

Publication Date : 2020-10-06

Article Type : Research Paper

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 $insert ignore into journalissuearticles values(0,T]\times\mathbb{R}.$ *********************************************************************************************************************************************** ***********************************************************************************************************************************************
Keywords : Fractional differential equations, mean value theorem, Nagumo type uniqueness, Peano type existence theorem