Dynamics and Stability Results for Hilfer Fractional Type Thermistor Problem
Abstract
:1. Introduction
2. Basic Concepts and Results
- The operator can be written asMoreover, the parameter satisfies
- The generalization (3) for coincides with the Riemann–Liouville derivative and for with the Caputo derivative
- If exists and in , thenFurthermore, if and , then
- If exists and in , then
- 1.
- 2.
- .
- 1.
- Definition 6⇒ Definition 7.
- 2.
- Definition 8⇒ Definition 9.
- 3.
- Definition 8 for ⇒ Definition 6.
3. Existence Results
4. The Ulam–Hyers–Rassias Stability
Acknowledgments
Author Contributions
Conflicts of Interest
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Vivek, D.; Kanagarajan, K.; Sivasundaram, S. Dynamics and Stability Results for Hilfer Fractional Type Thermistor Problem. Fractal Fract. 2017, 1, 5. https://doi.org/10.3390/fractalfract1010005
Vivek D, Kanagarajan K, Sivasundaram S. Dynamics and Stability Results for Hilfer Fractional Type Thermistor Problem. Fractal and Fractional. 2017; 1(1):5. https://doi.org/10.3390/fractalfract1010005
Chicago/Turabian StyleVivek, D., K. Kanagarajan, and Seenith Sivasundaram. 2017. "Dynamics and Stability Results for Hilfer Fractional Type Thermistor Problem" Fractal and Fractional 1, no. 1: 5. https://doi.org/10.3390/fractalfract1010005