HYERS-ULAM STABILITY ANALYSIS FOR PIECEWISE VARIABLE ORDER FRACTIONAL IMPULSIVE EVOLUTION SYSTEMS

Kamal Shah; Arshad Ali; M. Boukhobza; A. Debbouche; Thabet Abdeljawad

doi:10.11948/20240536

2025 Volume 15 Issue 5

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Kamal Shah, Arshad Ali, M. Boukhobza, A. Debbouche, Thabet Abdeljawad. HYERS-ULAM STABILITY ANALYSIS FOR PIECEWISE VARIABLE ORDER FRACTIONAL IMPULSIVE EVOLUTION SYSTEMS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 3159-3184. doi: 10.11948/20240536

Citation:

Kamal Shah, Arshad Ali, M. Boukhobza, A. Debbouche, Thabet Abdeljawad. HYERS-ULAM STABILITY ANALYSIS FOR PIECEWISE VARIABLE ORDER FRACTIONAL IMPULSIVE EVOLUTION SYSTEMS[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 3159-3184. doi: 10.11948/20240536

HYERS-ULAM STABILITY ANALYSIS FOR PIECEWISE VARIABLE ORDER FRACTIONAL IMPULSIVE EVOLUTION SYSTEMS

1.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2.
Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa 18800, Pakistan
3.
Department of Mathematics and Informatics, University of Mostaganem, Mostaganem 27000, Algeria
4.
Department of Mathematics, Guelma University, Guelma 24000, Algeria
5.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India
6.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
7.
Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Author Bio: Email: arshad.swatpk@gmail.com(A. Ali); Email: arboukhobza@gmail.com(M. Boukhobza)
Corresponding authors: Email: kamalshah408@gmail.com,kshah@psu.edu.sa(K. Shah); Email: amar_debbouche@yahoo.fr(A. Debbouche); Email: tabdeljawad@psu.edu.sa(T. Abdeljawad)

Abstract

Abstract

We investigate a class of piecewise variable-order fractional differential equations with impulsive and nonlocal conditions in Banach space. The nonhomogeneous term in the proposed system is given in terms of variable kernel which has flexibility property. We formulate appropriate equivalent integral equations to the considered evolution problem, then we show the solvability results by using mainly fractional calculus and fixed point techniques. Further, we study Hyers-Ulam stability analysis by adapting suitable conditions. The concerned area has numerous applications in those evolution processes and phenomenon, where abrupt changes occur. At the end, we support our obtained theory by illustrative and computational example.
- Evolution problem /
- piecewise fractional order derivative /
- impulsive conditions /
- variable kernel /
- Hyers-Ulam stability
MSC: 34A08, 34G20, 34D20

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References

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