Existence of Solutions to the Variable Order Caputo Fractional Thermistor Problem
Abstract
1. Introduction
2. Basic Concepts
- (i)
- is called a generalized interval if it is either a standard interval, a point, or ∅.
- (ii)
- If S is a generalized interval, then the finite set consisting of generalized intervals contained in S is called a partition of S provided that every lies in exactly one of the intervals in the finite set .
- (iii)
- We say that the function is piecewise constant with respect to the partition of S, if for any , ℵ is constant on .
3. Main Results
- ℵ is continuous;
- , , for all and ;
- , for all and ;
- For
4. An Example
5. Discussion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Graef, J.R.; Maazouz, K.; Pinelas, S.; Bellabes, Z.; Boussekkine, N. Existence of Solutions to the Variable Order Caputo Fractional Thermistor Problem. Fractal Fract. 2025, 9, 139. https://doi.org/10.3390/fractalfract9030139
Graef JR, Maazouz K, Pinelas S, Bellabes Z, Boussekkine N. Existence of Solutions to the Variable Order Caputo Fractional Thermistor Problem. Fractal and Fractional. 2025; 9(3):139. https://doi.org/10.3390/fractalfract9030139
Chicago/Turabian StyleGraef, John R., Kadda Maazouz, Sandra Pinelas, Zineb Bellabes, and Naima Boussekkine. 2025. "Existence of Solutions to the Variable Order Caputo Fractional Thermistor Problem" Fractal and Fractional 9, no. 3: 139. https://doi.org/10.3390/fractalfract9030139
APA StyleGraef, J. R., Maazouz, K., Pinelas, S., Bellabes, Z., & Boussekkine, N. (2025). Existence of Solutions to the Variable Order Caputo Fractional Thermistor Problem. Fractal and Fractional, 9(3), 139. https://doi.org/10.3390/fractalfract9030139