Boundary Value Problem for Fractional q-Difference Equations with Integral Conditions in Banach Spaces

The authors investigate the existence of solutions to a class boundary value problems for fractional q-difference equations in Banach space that involves q-derivative Caputo type and nonlinear integral conditions. Their result is based on Mönch’s fixed point theorem technique measures noncompactness. This approach has proved be an interesting useful studying such problems. Some basic concepts from q-calculus are introduced, including q-derivatives q-integrals. An example main included as well some suggestions future research.