Hybrid Initial Value Problems of Fractional Order with q -Derivatives

Abstract

In the present article, it has been tried to extend the theory of q-fractional hybrid differential equations that entails Riemann–Liouville q-differential operators. We have also attempted to prove an existence theorem for FHDEs under Lipschitz and Caratheodory conditions. We have also presented some fundamental fractional differential inequalities that can be employed to indicate that some external solutions exist for such problems. The required tools are taken into consideration and the principle for comparison is offered which can be used to conduct further research work regarding qualitative behavior of solutions.