Investigation of a Fractional q-Integral Equation

Abstract This research delves into a specific class of fractional integral equations that incorporate the Riemann-Liouville fractional q-integral. The study utilizes two major mathematical tools: Schauder’s fixed-point theorem and Banach’s contraction mapping principle, to analyze these equations. By applying these methods, we establish robust criteria that guarantee both the existence and uniqueness of solutions to the fractional q-integral equations under consideration. The work places particular emphasis on the use of the Riemann-Liouville framework for fractional derivatives and integrals, highlighting its significance in defining and analyzing fractional q-integrals. The results of this investigation contribute to the theoretical advancement of fractional calculus, particularly in the setting of q-integrals, which are crucial in diverse applications across mathematics and applied sciences.