The Existence and Stability of Integral Fractional Differential Equations
Abstract
1. Introduction
2. Preliminaries
3. Main Results
- Let and be continuous functions.
- is continuous, and there exist constants and , with .
- ,
- : there exist non-decreasing functions such that
- where .
- , where .For simplicity,
- Step 1: First, we demonstrate that . Consider . For each , we have
- Step 2: We prove the continuity of . In the set , let us consider the sequence converging to ν. Consequently, for any ,
- Step 3: It is evident from this that the operator is uniformly bounded. Now, we present the equicontinuity of . For this, we suppose such that . We have
4. Stability
5. Example
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Khan, R.U.; Popa, I.-L. The Existence and Stability of Integral Fractional Differential Equations. Fractal Fract. 2025, 9, 295. https://doi.org/10.3390/fractalfract9050295
Khan RU, Popa I-L. The Existence and Stability of Integral Fractional Differential Equations. Fractal and Fractional. 2025; 9(5):295. https://doi.org/10.3390/fractalfract9050295
Chicago/Turabian StyleKhan, Rahman Ullah, and Ioan-Lucian Popa. 2025. "The Existence and Stability of Integral Fractional Differential Equations" Fractal and Fractional 9, no. 5: 295. https://doi.org/10.3390/fractalfract9050295
APA StyleKhan, R. U., & Popa, I.-L. (2025). The Existence and Stability of Integral Fractional Differential Equations. Fractal and Fractional, 9(5), 295. https://doi.org/10.3390/fractalfract9050295