Existence of Solutions for Fractional Order Differential Equations: Extended Results

Authors

  • Saleh Aljurbua Department of Mathematics., College of Science., Qassim University https://orcid.org/0009-0004-1971-9418
  • Munirah Alrashidi Department of Mathematics., College of Science., Qassim University
  • Asrar Alrashidi Department of Mathematics., College of Science., Qassim University
  • Reham Alharbi Department of Mathematics., College of Science., Qassim University
  • Rawan Almutairi Department of Mathematics., College of Science., Qassim University
  • Majd Saad Department of Mathematics., College of Science., Qassim University
  • Najla Alharbi Department of Mathematics., College of Science., Qassim University
  • Wejdan Alrawji Department of Mathematics., College of Science., Qassim University
  • Najd Alharbi Department of Mathematics., College of Science., Qassim University
  • Dhay Alharbi Department of Mathematics., College of Science., Qassim University
  • Rawan Alashwan Department of Mathematics., College of Science., Qassim University
  • Asamh Alluhayb Department of Mathematics., College of Science., Qassim University
  • Nuha Alfuraih Department of Mathematics., College of Science., Qassim University

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5935

Keywords:

fractional derivatives; differential equations; fractional differential equations; antiperiodic; nonlocal boundary conditions; existence.

Abstract

This study investigates the existence of solutions for nonlinear fractional differential equations of order $ q \in (1, 2]$. We establish new existence results for the boundary conditions $\xi(\kappa) = \alpha\neq 0$ and $\xi(\omega)= \beta \neq 0$ by incorporating an intermediate point, extending existing methodologies. Our results rely on fixed point theorems and the contraction principle, which provide a robust framework for analyzing these equations. We also provide several illustrative examples to demonstrate our results, showcasing their relevance in theoretical and applied contexts.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Differential Equations

License

Copyright (c) 2025 Saleh Aljurbua, Munirah Alrashidi, Asrar Alrashidi, Reham Alharbi, Rawan Almutairi, Majd Saad, Najla Alharbi, Wejdan Alrawji, Najd Alharbi, Dhay Alharbi, Rawan Alashwan, Asamh Alluhayb, Nuha Alfuraih

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How to Cite

Existence of Solutions for Fractional Order Differential Equations: Extended Results. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5935. https://doi.org/10.29020/nybg.ejpam.v18i2.5935