Generalized Caputo Fractional Proportional Differential Equations and Inclusion Involving Slit-Strips and Riemann-Stieltjes Integral Boundary Conditions

Authors

  • Wafa Shammakh Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 13151, Jeddah 21493, Saudi Arabia https://orcid.org/0000-0002-5926-2182
  • Hanan A. Alyami Mathematics Department, Deanship of Preparatory Year, Najran University, P.O. Box 1988, Najran 11001, Saudi Arabia
  • Hadeel Z. Alzumi Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 13151, Jeddah 21493, Saudi Arabia https://orcid.org/0000-0002-9291-1420

DOI:

https://doi.org/10.37256/cm.5220244100

Keywords:

generalzied fractional proportional derivatives, integral boundary conditions, fractional differential equations and inclusions, fixed-point theorems

Abstract

The main purpose of this study is to investigate the existence and uniqueness of solutions to a nonlocal boundary value problem. This newly defined class involves nonlinear fractional differential equations of general proportional fractional derivative and integral with respect to another function. Additionally, the inclusion case results associated to our problem are discussed. Our analysis relies on fixed point theorems and fractional calculus techniques. By giving examples, the obtained results are clearly illustrated.

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Published

2024-04-17

Issue

Contemporary Mathematics, Volume 5 Issue 2 (2024), 1122-2592

Section

Research Article

Categories

License

Copyright (c) 2024 Wafa Shammakh, et al.

Creative Commons License

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

How to Cite

1.
Generalized Caputo Fractional Proportional Differential Equations and Inclusion Involving Slit-Strips and Riemann-Stieltjes Integral Boundary Conditions. Contemp. Math. [Internet]. 2024 Apr. 17 [cited 2025 Dec. 24];5(2):1711-49. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/4100