EXISTENCE RESULT FOR A COUPLED SYSTEM OF HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS IN A BANACH ALGEBRA

In this work, we investigate the existence result for a coupled system of hybrid fractional differential equations in a Banach algebra. Our main result is based on a generalization of Darbo’s fixed point theorem in Banach algebra. We apply in our approach the technique of measure of non-compactness, we prove that the Kuratowski measure of noncompactness satisfies a condition (m) which will be useful in our considerations. An example is given to illustrate the feasibility of our main result. An example is provided to illustrate our result.