Abstract
This paper is devoted by developing some necessary and sufficient conditions required for the existence of at least one solution to a highly nonlinear toppled system of fractional order boundary value problems with integral boundary conditions. By the use of classical fixed point theorems like Banach contraction theorem, nonlinear alternative of Leray–Schauder type and fixed point theorem of cone expansion and contraction of norm type, we establish sufficient conditions for the existence as well as for uniqueness of solution to the system under consideration. Further, we also discuss Hyers–Ullam stability for the considered toppled system. Also, some examples are provided to demonstrate our main results.
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