Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions

ψ-Hilfer Fractional Implicit Differential Equation

https://doi.org/10.48185/jmam.v1i1.4

Authors

  • Mohammed A. Almalahi Dr. Babasaheb Ambedkar Marathwada University
  • Satish. K Panchal Dr. Babasaheb Ambedkar Marathwada University

Keywords:

Fractional differential equations, Fractional derivatives, Mittag-Leffler functions, Ulam stability, Fixed point theorem.

Abstract

In this paper, we study the class of boundary value problems for a nonlinear implicit fractional differential equation with periodic conditions involving a ψ-Hilfer fractional derivative. With the help of properties Mittag-Leffler functions, and fixed-point techniques, we establish the existence and uniqueness results, whereas the generalized Gronwall inequality is applied to get the stability results. Also, an example is provided to illustrate the obtained results.

 

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Published

2020-12-03

How to Cite

Almalahi, M. A., & Panchal, S. K. (2020). Some existence and stability results for ψ-Hilfer fractional implicit differential equation with periodic conditions: ψ-Hilfer Fractional Implicit Differential Equation. Journal of Mathematical Analysis and Modeling, 1(1), 1–19. https://doi.org/10.48185/jmam.v1i1.4

Issue

Vol. 1 No. 1 (2020): 2020 (1)

Section

Articles
Copyright & Licensing

Copyright (c) 2020 Mohammed A. Almalahi, Satish. K Panchal

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.