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Existence of Solutions for a Coupled System of Nonlinear Implicit Differential Equations Involving \(\varrho \)-Fractional Derivative with Anti Periodic Boundary Conditions

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Abstract

This paper is concerned with a new class of coupled implicit systems involving \(\varrho \)-fractional derivatives of different orders and anti periodic boundary conditions. We first convert the given implicit problem into a fixed point problem and then apply the fixed point theorems due to Krasnoselskii and Banach to establish the existence and uniqueness of its solutions. Examples are given for the illustration of the main results.

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Acknowledgements

The authors thank the reviewers for their useful comments on their work.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences & Arts, King Abdulaziz University, Rabigh, 21911, Saudi Arabia

    Madeaha Alghanmi

  2. Department of Mathematics, Texas A& M University, Kingsville, Texas, 78363-8202, USA

    Ravi P. Agarwal

  3. 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. Madeaha Alghanmi
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Correspondence to Ravi P. Agarwal.

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Alghanmi, M., Agarwal, R.P. & Ahmad, B. Existence of Solutions for a Coupled System of Nonlinear Implicit Differential Equations Involving \(\varrho \)-Fractional Derivative with Anti Periodic Boundary Conditions. Qual. Theory Dyn. Syst. 23, 6 (2024). https://doi.org/10.1007/s12346-023-00861-5

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