Existence and uniqueness of solutions for multi-term fractional q-integro-differential equations via quantum calculus

In this investigation, by applying the definition of the fractional q-derivative of the Caputo type and the fractional q-integral of the Riemann-Liouville type, we study the existence and uniqueness of solutions for a multi-term nonlinear fractional q-integro-differential equations under some boundary conditions Dq alpha cx(t)=w(t,x(t),(phi 1x)(t),(phi 2x)(t),cDq beta 1x(t),cDq beta 2x(t),...,cDqbeta nx(t)). Our results are based on some classical fixed point techniques, as Schauder's fixed point theorem and Banach contraction mapping principle. Besides, some instances are exhibited to illustrate our results and we report all algorithms required along with the numerical result obtained.