Existence of Solutions to Fractional Differential Equations with Mixed Caputo–Riemann Derivative
Abstract
1. Introduction
2. Preliminaries
3. Main Result
- (A1) ∃ a positive constant , s.tand .
- (A2) s.t and .
- (A3) ∃ an increasing function and s.t for any .
- Therefore, .
- By fixing , where , and with , we can prove that the operator is completely continuous.
3.1. Stability Theorems
3.2. Example
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Almatarneh, M.; Zorlu, S.; Mahmudov, N.I. Existence of Solutions to Fractional Differential Equations with Mixed Caputo–Riemann Derivative. Fractal Fract. 2025, 9, 374. https://doi.org/10.3390/fractalfract9060374
Almatarneh M, Zorlu S, Mahmudov NI. Existence of Solutions to Fractional Differential Equations with Mixed Caputo–Riemann Derivative. Fractal and Fractional. 2025; 9(6):374. https://doi.org/10.3390/fractalfract9060374
Chicago/Turabian StyleAlmatarneh, Mahir, Sonuc Zorlu, and Nazim I. Mahmudov. 2025. "Existence of Solutions to Fractional Differential Equations with Mixed Caputo–Riemann Derivative" Fractal and Fractional 9, no. 6: 374. https://doi.org/10.3390/fractalfract9060374
APA StyleAlmatarneh, M., Zorlu, S., & Mahmudov, N. I. (2025). Existence of Solutions to Fractional Differential Equations with Mixed Caputo–Riemann Derivative. Fractal and Fractional, 9(6), 374. https://doi.org/10.3390/fractalfract9060374