Abstract
We study a conformable fractional nonlocal thermistor problem on time scales. Under an appropriate nonrestrictive condition on the resistivity function, we establish existence and uniqueness results. The proof is based on the use of Schauder’s point fixed theorem.
Highlights
Fractional calculus has aroused keen considerable attention of several researchers with many emerging applications, including memory effects and future dependence, in mathematical physics, biology, dynamical systems, chemistry, population dynamics, and recently in epidemic diseases [2, 3, 6, 9,10,11, 15, 16, 21, 23, 25, 26].The theory of time scales is often used for describing models that cannot be considered as exclusively continuous or exclusively discrete processes
To find out more about the fractional calculus on a time scale, excellent references are situated in the books of Miller and Ross [22] and Podlubny [24]
The notion of conformable fractional derivative, which is a natural extension of the classical derivative, was initiated in [20]
Summary
Fractional calculus has aroused keen considerable attention of several researchers with many emerging applications, including memory effects and future dependence, in mathematical physics, biology, dynamical systems, chemistry, population dynamics, and recently in epidemic diseases [2, 3, 6, 9,10,11, 15, 16, 21, 23, 25, 26].The theory of time scales is often used for describing models that cannot be considered as exclusively continuous or exclusively discrete processes. Due to its various applications, a great interest is given by researchers to the study of integer order, fractional order, or time scales thermistors models via different approaches [7, 28, 30, 31]. In [28], the question of existence and uniqueness of a positive solution to generalized nonlocal thermistor problems with fractional order derivatives was investigated. Global existence of solutions for a fractional nonlocal thermistor problem in the Caputo sense was addressed in [27].
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