BASHIR AHMAD

In this paper, we introduce and investigate a new class of nonlinear multi-term impulsive anti-periodic boundary value problems involving Caputo type fractional [Formula: see text]-derivative operators of different orders and the Riemann–Liouville fractional [Formula: see text]-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.

We investigate the existence criteria for solutions of a nonlinear coupled system of Hilfer–Hadamard fractional differential equations of different orders complemented with nonlocal coupled Hadamard fractional integral boundary conditions. The desired results are accomplished with the aid of standard fixed-point theorems. We emphasize that the fixed point approach is one of the effective methods to establish the existence results for boundary value problems. Examples illustrating the obtained results are constructed.