Existence results for fractional hybrid differential systems in Banach algebras

Abstract

In this manuscript we investigate the existence of solutions for the following system of fractional hybrid differential equations (FHDEs): {D-p [theta(t) w(t,theta(t))/u(t,theta(t))] = v(t, v(t)), t is an element of J, D-p [v(t)-w(t, v, (t))/u(t, v(t))] = v(t, theta(t)), t is an element of J, 0 ˂ p ˂ 1, theta(0) = 0, v(0) = 0, where Dr denotes the Riemann-Liouville fractional derivative of order r, J = [0, 1], and the functions u : J x R -˃ R \ {0}, w : J x R -˃ R, (0, 0) = 0 nd v : J x R -˃ R satisfy certain conditions. Here, we extend the Dhage hybrid fixed point theorem (Dhage in Kyungpook Math. J. 44: 145-155, 2004) and then present some results on the existence of coupled fixed points for a category of operators in Banach algebra. Also, an example is analyzed to show the use of the reported results.