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Generalized Fractional Differential Systems with Stieltjes Boundary Conditions

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Abstract

In this work, we study the existence of solutions to a new class of boundary value problems consisting of a system of nonlinear differential equations with generalized fractional derivative operators of different orders and nonlocal boundary conditions containing Riemann-Stieltjes and generalized fractional integral operators. We emphasize that the nonlinearities in the given system are of general form as they depend on the unknown functions as well as their lower order generalized fractional derivatives. The uniqueness result for the given problem is proved by applying the Banach contraction mapping principle, while the existence of solutions for the given system is shown with the aid of Leray-Schauder alternative. Two concrete examples are given for illustrating the obtained results. The paper concludes with some interesting observations.

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Acknowledgements

The authors would like to thank the referees for their suggestions and helpful comments which improved the presentation of the original manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Razi University, 67149, Kermanshah, Iran

    Nemat Nyamoradi

  2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Bashir Ahmad

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  1. Nemat Nyamoradi
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Nyamoradi, N., Ahmad, B. Generalized Fractional Differential Systems with Stieltjes Boundary Conditions. Qual. Theory Dyn. Syst. 22, 6 (2023). https://doi.org/10.1007/s12346-022-00703-w

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