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Existence and uniqueness of solutions for a coupled system of sequential fractional differential equations with initial conditions

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Abstract

In this paper, we consider a coupled system of sequential fractional differential equations associated with initial conditions. The main theorems provide new existence and uniqueness conditions for solutions of the proposed coupled system. We conclude an immediate consequence that establishes weaker conditions to ensure the existence and uniqueness of solutions for the corresponding sequential fractional differential equation. Meanwhile, an iterative sequence is constructed in terms of solution operator that converges to the unique fixed point which corresponds to the unique solution. The consistency of the main results is verified by presenting two numerical examples. For the sake of completeness, we end the paper with a concluding remark.

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Acknowledgements

The authors would like to thank the editor who handled our paper during the reviewing process. Particular thanks go to the anonymous referees who read, review and evaluate our work. The second author like to thank Prince Sultan University for supporting this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) Group Number RG-DES-2017-01-17.

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Authors and Affiliations

  1. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    Hamid Baghani

  2. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

    Jehad Alzabut

  3. Department of Basic Sciences, Birjand University of Technology, Birjand, Iran

    Javad Farokhi-Ostad

  4. Department of Statistics, Mathematical Analysis and Optimization, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto

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  1. Hamid Baghani
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  2. Jehad Alzabut
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  3. Javad Farokhi-Ostad
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  4. Juan J. Nieto
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Correspondence to Hamid Baghani.

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Baghani, H., Alzabut, J., Farokhi-Ostad, J. et al. Existence and uniqueness of solutions for a coupled system of sequential fractional differential equations with initial conditions. J. Pseudo-Differ. Oper. Appl. 11, 1731–1741 (2020). https://doi.org/10.1007/s11868-020-00359-7

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  • DOI: https://doi.org/10.1007/s11868-020-00359-7

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