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Study of Solution to a Toppled System of Fractional Differential Equations with Integral Boundary Conditions

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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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Acknowledgments

We are really thankful to the suggestions and comments point out by the anonymous referee, which improved the quality of this paper.

Authors’ Contributions   All authors equally contributed the MS and approved the final version.

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  1. Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan

    Kamal Shah & Rahmat Ali Khan

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  1. Kamal Shah
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Correspondence to Kamal Shah.

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Shah, K., Khan, R.A. Study of Solution to a Toppled System of Fractional Differential Equations with Integral Boundary Conditions. Int. J. Appl. Comput. Math 3, 2369–2388 (2017). https://doi.org/10.1007/s40819-016-0243-y

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