SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETRIC TYPE ANTI-PERIODIC BOUNDARY CONDITIONS

Bashir Ahmad; Sotiris K. Ntouyas; Ahmed Alsaedi; Khalid A. Alalwi

doi:10.11948/20240511

2025 Volume 15 Issue 5

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Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi, Khalid A. Alalwi. SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETRIC TYPE ANTI-PERIODIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2921-2934. doi: 10.11948/20240511

Citation:

Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi, Khalid A. Alalwi. SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETRIC TYPE ANTI-PERIODIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2921-2934. doi: 10.11948/20240511

SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETRIC TYPE ANTI-PERIODIC BOUNDARY CONDITIONS

1.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Author Bio: sntouyas@uoi.gr(S. K. Ntouyas); aalsaedi@hotmail.com(A. Alsaedi); kalalawi0006@stu.kau.edu.sa(K. A. Alalwi)
Corresponding author: Email: bashirahmadqau@yahoo.com(B. Ahmad)

Abstract

Abstract

We discuss the existence and uniqueness of solutions for sequential fractional differential equations supplemented with parametric type anti-periodic boundary conditions. We make use of fixed point theorems due to $ {\rm{Krasnosel'ski\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i}}}$ and Banach to obtain the desired results. Examples illustrating the obtained results are presented. Moreover, an interesting feature concerning the solutions of parametric type anti-periodic boundary value problems of lower and higher order sequential fractional differential equations is presented (see the conclusions section). Our results are novel in the given configuration and generalize the literature on anti-periodic boundary value problems.
- Sequential fractional differential equation /
- parametric /
- antiperiodic boundary conditions /
- existence /
- fixed point
MSC: 34A08, 34B10, 34B15

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References

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