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Stability Analysis and Existence Criteria with Numerical Illustrations to Fractional Jerk Differential System Involving Generalized Caputo Derivative

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Abstract

This inquire about ponder is committed to investigating a few properties in connection to behaviors of solutions to an extended fractional structure of the standard jerk equation. Here, we define the scheme of the general fractional jerk problem using the generalized G operators. The existence result of such a new model is derived and analyzed based on some inequalities and fixed point tools. Furthermore, analysis of its Ulam–Hyers–Rassias type stability is performed and finally, we give numerical simulations for the existing parameters of the mentioned fractional G-jerk system in the Katugampola, Caputo–Hadamard and Caputo settings under different arbitrary orders.

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Acknowledgements

The third and fifth authors were supported by Azarbaijan Shahid Madani University. J. Alzabut is thankful to Prince Sultan University and OSTİM Technical University for their endless support for writing this paper.

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Authors and Affiliations

  1. Department of Mathematics, Al-Azhar University-Gaza, Gaza Strip, Palestine

    Mohammed M. Matar

  2. Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, 65178-38695, Iran

    Mohammad Esmael Samei

  3. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Sina Etemad & Shahram Rezapour

  4. Laboratory of Applied Mathematics, University of Kasdi Merbah, Ouargla, 30000, Algeria

    Abdelkader Amara

  5. Department of Mathematics, Kyuing Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea

    Shahram Rezapour

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

    Shahram Rezapour

  7. Department of Industrial Engineering, OSTÍM Technical University, 06374, Ankara, Turkey

    Jehad Alzabut

  8. Department of Mathematics and General Sciences, Prince Sultan University, 12435, Riyadh, Saudi Arabia

    Jehad Alzabut

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  1. Mohammed M. Matar
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  4. Abdelkader Amara
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Contributions

All authors have equal contributions. All authors read and approved the final manuscript. MMM: Initial draft, methodology, actualization, formal analysis, validation, investigation, and initial draft. MES: Actualization, formal analysis, validation, investigation, software, simulation, and was a major contributor in writing the manuscript. SE: Actualization, methodology, formal analysis, validation, investigation, software, simulation, initial draft and was a major contributor in writing the manuscript. AA: Actualization, validation, methodology, formal analysis, investigation, and initial draft. SR: Validation, methodology, actualization, formal analysis, investigation, and initial draft. JA: Investigation, initial draft, formal analysis, actualization, methodology, validation, and supervision of the original draft and editing. All authors read and approved the final manuscript.

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Correspondence to Mohammad Esmael Samei or Shahram Rezapour.

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Matar, M.M., Samei, M.E., Etemad, S. et al. Stability Analysis and Existence Criteria with Numerical Illustrations to Fractional Jerk Differential System Involving Generalized Caputo Derivative. Qual. Theory Dyn. Syst. 23, 111 (2024). https://doi.org/10.1007/s12346-024-00970-9

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