Bouharket Bendouma, Amin Benaissa Cherif, Ahmed Hammoudi

Existence of Solutions for Nonlocal Nabla Conformable Fractional Thermistor Problem on Time Scales

In this paper, we study the existence of solution for the nonlocal nabla conformable fractional thermistor problem of order $\alpha $ on an arbitrary bounded time scale. By a result of the work, the thermistor equation has been generalized on the time scale by using conformable fractional. The study is carried out by using the tube solution (a generalization of lower and upper solutions) and Schauder's fixed-point theorem. Finally, an example is given to illustrate the results of this work.

Mathematics Subject Classification: 34N05, 34A08, 34B15, 26A33, 26E70

Key words and phrases: Fractional nonlocal thermistor problems, nabla conformable fractional calculus on time scales, solution-tube, Schauder's fixed-point