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Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative

Author

Listed:
  • Mohamed Jleli

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Bessem Samet

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Calogero Vetro

    (Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy)

Abstract

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis of the integral form of the inequality with appropriate choice of test function.

Suggested Citation

  • Mohamed Jleli & Bessem Samet & Calogero Vetro, 2021. "Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative," Mathematics, MDPI, vol. 9(16), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1866-:d:609464
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    References listed on IDEAS

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    1. Qureshi, Sania, 2020. "Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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