INVESTIGATION OF A NONLINEAR MULTI-TERM IMPULSIVE ANTI-PERIODIC BOUNDARY VALUE PROBLEM OF FRACTIONAL q-INTEGRO-DIFFERENCE EQUATIONS

In this paper, we introduce and investigate a new class of nonlinear multi-term impulsive anti-periodic boundary value problems involving Caputo type fractional q-derivative operators of different orders and the Riemann-Liouville fractional q-integral operator. The uniqueness of solutions to the given problem is proved with the aid of Banach's fixed point theorem. Applying a Shaefer-like fixed point theorem, we also obtain an existence result for the problem at hand. Examples are constructed for illustrating the obtained results. The paper concludes with certain interesting observations concerning the reduction of the results proven in the paper to some new results under an appropriate choice of the parameters involved in the governing equation.

Automated summary

In this paper, a new class of nonlinear multi-term impulsive anti-periodic boundary value problems involving Caputo type fractional q-derivative operators of different orders and the Riemann-Liouville fractional q-integral operator is introduced and investigated. The uniqueness of solutions to the given problem is proved with the aid of Banach's fixed point theorem. An existence result for the problem is also obtained by applying a Shaefer-like fixed point theorem. Examples are constructed to illustrate the obtained results.