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Non-existence Results for a Nonlinear Fractional System of Differential Problems

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Abstract

The non-existence of solutions is discussed for a system of fractional differential equations including two types of fractional derivatives: the Caputo fractional derivative (CFD) and the Riemann–Liouville fractional derivative (RLFD). The nonlinear sources are nonlocal in time. The system we consider is more general than those previously discussed in the literature. Our results are obtained by using several properties of fractional derivatives, the test-function method and by applying some integral inequalities. Finally, we provide some examples to illustrate our findings.

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Acknowledgements

The author T. Abdeljawad would like to thank Prince Sultan University for the support through the TAS research lab.

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Authors and Affiliations

  1. Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 34151, Dammam, Saudi Arabia

    Mohammed D. Kassim

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

    Thabet Abdeljawad

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

    Thabet Abdeljawad

  4. Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Republic of Korea

    Thabet Abdeljawad

  5. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Garankuwa, Medusa, 0204, South Africa

    Thabet Abdeljawad

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  1. Mohammed D. Kassim
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Kassim, M.D., Abdeljawad, T. Non-existence Results for a Nonlinear Fractional System of Differential Problems. Qual. Theory Dyn. Syst. 23, 17 (2024). https://doi.org/10.1007/s12346-023-00869-x

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