Exploring Impulsive and Delay Differential Systems Using Piecewise Fractional Derivatives
Abstract
1. Introduction
2. Basic Results
3. Solution Representation of Problem (1)
4. Existence of Solutions
- (H1)
- For function g, the constants satisfy the Lipschitz conditionFor the term we use the following relations:
- (H2)
- Let be continuous such that
- (H3)
- There exist bounded functions such that
- (H4)
- There exist such that
- (H5)
- There exists constant such that
- (H6)
- We assume that
5. Ulam–Hyers (U-H) Stability
6. Application
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Saber, H.; Ali, A.; Aldwoah, K.; Alraqad, T.; Moumen, A.; Alsulami, A.; Eljaneid, N. Exploring Impulsive and Delay Differential Systems Using Piecewise Fractional Derivatives. Fractal Fract. 2025, 9, 105. https://doi.org/10.3390/fractalfract9020105
Saber H, Ali A, Aldwoah K, Alraqad T, Moumen A, Alsulami A, Eljaneid N. Exploring Impulsive and Delay Differential Systems Using Piecewise Fractional Derivatives. Fractal and Fractional. 2025; 9(2):105. https://doi.org/10.3390/fractalfract9020105
Chicago/Turabian StyleSaber, Hicham, Arshad Ali, Khaled Aldwoah, Tariq Alraqad, Abdelkader Moumen, Amer Alsulami, and Nidal Eljaneid. 2025. "Exploring Impulsive and Delay Differential Systems Using Piecewise Fractional Derivatives" Fractal and Fractional 9, no. 2: 105. https://doi.org/10.3390/fractalfract9020105
APA StyleSaber, H., Ali, A., Aldwoah, K., Alraqad, T., Moumen, A., Alsulami, A., & Eljaneid, N. (2025). Exploring Impulsive and Delay Differential Systems Using Piecewise Fractional Derivatives. Fractal and Fractional, 9(2), 105. https://doi.org/10.3390/fractalfract9020105