EXISTENCE OF SOLUTIONS FOR HYBRID FRACTIONAL PANTOGRAPH EQUATIONS

Abstract

In this paper, we study the existence of the hybrid fractional pantograph equation where α, µ, σ ∈ (0, 1) and D α 0 + denotes the Riemann-Liouville fractional derivative. The results are obtained using the technique of measures of noncompactness in the Banach algebras and a fixed point theorem for the product of two operators verifying a Darbo type condition. Some examples are provided to illustrate our results