FRACTIONAL HYBRID INITIAL VALUE PROBLEM FEATURING q-DERIVATIVES.

We have perused about the existence of a solution toward hybrid initial value problem (HIVP) featuring fractional q-derivative ... in which D948q denotes the Riemann-Liouville fractional q-derivative in the order of δ. In Banach algebra, by making use of a fixed point theorem based Dhage along with mixed Lipschitz and Caratheodory condition, a way of solving the above fractional Hybrid initial value problem (FHIVP) featuring q-derivatives verified, in this study. [ABSTRACT FROM AUTHOR]