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Implicit Fractional Differential Equations via the Liouville–Caputo Derivative

Author

Listed:
  • Juan J. Nieto

    (Department of Mathematical Analysis, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
    Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Abelghani Ouahab

    (Laboratory of Mathematics, Sidi-Bel-Abbès University, P.O. Box 89, Sidi-Bel-Abbès 22000, Algeria)

  • Venktesh Venktesh

    (Department of Mathematical Analysis, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
    Birla Institute of Technology & Science, Pilani 333031, India)

Abstract

We study an initial value problem for an implicit fractional differential equation with the Liouville–Caputo fractional derivative. By using fixed point theory and an approximation method, we obtain some existence and uniqueness results.

Suggested Citation

  • Juan J. Nieto & Abelghani Ouahab & Venktesh Venktesh, 2015. "Implicit Fractional Differential Equations via the Liouville–Caputo Derivative," Mathematics, MDPI, vol. 3(2), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:2:p:398-411:d:50086
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    Cited by:

    1. Ahmed M. A. El-Sayed & Sheren A. Abd El-Salam & Hind H. G. Hashem, 2022. "Global Existence for an Implicit Hybrid Differential Equation of Arbitrary Orders with a Delay," Mathematics, MDPI, vol. 10(6), pages 1-13, March.

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