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Investigation of fractional order inclusion problem with Mittag-Leffler type derivative

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Abstract

Inclusions problems due to differential equations arise in many situations like variational inequalities, projective dynamical systems, and many more. Therefore, the said area has given proper attentions in the last many years. The mentioned area has been extended to fractional order problems recently. The inclusion problems under the usual Caputo and Reimann-Liouville derivatives have been studied in literature very well. Therefore, inspired from the mentioned importance, we investigate a class of fractional order inclusion problems involving Atangana-Baleanu-Caputo derivative under boundary conditions. Our analysis is devoted to develop sufficient conditions for the existence theory of solution by using fixed point theory. For the illustration of our results, we give two suitable examples.

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Acknowledgements

“The authors Kamal Shah, and Thabet Abdeljawad would like to thank Prince Sultan University for the support through the TAS research lab".

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Authors and Affiliations

  1. Laboratory of SD, Faculty of Mathematics, University of Science and Technology Houari Boumediene, P.O. Box 32, El-Alia, Bab Ezzouar, 16111, Algiers, Algeria

    Adel Lachouri

  2. Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen

    Mohammed S. Abdo

  3. Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, 41000, Souk Ahras, Algeria

    Abdelouaheb Ardjouni

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

    Kamal Shah & Thabet Abdeljawad

  5. Department of Mathematics, University of Malakand, Chakdara, Dir (Lower), Khyber Pakhtunkhawa, 18000, Pakistan

    Kamal Shah

  6. Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

    Thabet Abdeljawad

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  1. Adel Lachouri
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  2. Mohammed S. Abdo
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  3. Abdelouaheb Ardjouni
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  4. Kamal Shah
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  5. Thabet Abdeljawad
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Correspondence to Thabet Abdeljawad.

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Lachouri, A., Abdo, M.S., Ardjouni, A. et al. Investigation of fractional order inclusion problem with Mittag-Leffler type derivative. J. Pseudo-Differ. Oper. Appl. 14, 43 (2023). https://doi.org/10.1007/s11868-023-00537-3

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  • DOI: https://doi.org/10.1007/s11868-023-00537-3

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