ON THE EXISTENCE AND UNIQUENESS RESULTS FOR NONLINEAR SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS

چکیده مقاله

This paper is devoted to proving the existence, uniqueness and smoothness of solutions for differential equations with Riemann-Liouville sequential fractional derivatives admit-ting only the existence of a lower solution. The appropriate fractional Sobolev spaces equipped with a suitable partial order are introduced, and applying some fixed point theorems the results are proved. The approximate solutions are presented to the corresponding initial value problems. A few illustrative examples are given. © 2018, Institute of Applied Mathematics of Baku State University. All rights reserved.