ON EXTREMAL SOLUTIONS OF WEIGHTED FRACTIONAL HYBRID DIFFERENTIAL EQUATIONS

Abstract

In this article, focuses study the existence of solution for an initial
value problem of nonlinear fractional hybrid differential equations involving
Riemann-Liouville derivative in weighted space of continuous functions.
An existence theorem for this equation is proved under mixed Lipschitz and
Carath´eodory conditions. Some fundamental fractional differential inequalities
which are utilized to prove the existence of extremal solutions are also
established. Necessary tools are considered and the comparison principle is
proved which existes a minimal and maximal positive solutions.