Existence and continuation of solutions of Hilfer fractional differential equations

Document Type : Research Article


Department of mathematics, Institute of Chemical Technology, Mumbai--400 019 (M.S.), India


In the present paper we consider initial value problems for Hilfer fractional differential equations and for system of Hilfer fractional differential equations. By using equivalent integral equations and some fixed point theorems, we study the local existence of solutions. We extend these local existence results globally with the help of continuation theorems and generalized Gronwall inequality.