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Theoretical analysis demonstrates the existence of solutions in fractional thermistor models, indicating the utility of Hausdorff calculus and tube solution methods.
In this work, we examine the existence of solutions for the fractional thermistor problem involving the Hausdorff derivative. Our approach leads to a generalized thermistor model formulated within the framework of Hausdorff fractional calculus. To establish the existence of solutions, we employ the Schauder fixed-point theorem in conjunction with the tube solution method, which extends the classical concepts of lower and upper solutions. Finally, an illustrative example is presented to demonstrate the applicability of the obtained results.
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Ladrani et al. (2026) studied this question.
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