**Bouharket Bendouma, Amin Benaissa Cherif, Ahmed Hammoudi**

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

**abstract:**

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