Dynamics and Stability Results for Hilfer Fractional Type Thermistor Problem

Abstract

Abstract:In this paper, we study the dynamics and stability of thermistor problem for Hilfer fractional type. Classical fixed point theorems are utilized in deriving the results.

Existence and uniqueness results on time scales for fractional nonlocal thermistor problem in the conformable sense

“…Global existence of solutions for a fractional nonlocal thermistor problem in the Caputo sense was addressed in [27]. Existence and uniqueness results for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary nonempty closed subsets of the real numbers were studied in [29], Dynamics and stability results for Hilfer fractional derivative, which interpolate both the Riemann-Liouville and the Caputo fractional derivative, thermistor problems were investigated in [33]. Existence of a particular tube solution of a nonlocal thermistor problem for fractional derivative in the conformable sense was proved in [32].…”

On the (k,s)-Hilfer-Prabhakar Fractional Derivative With Applications to Mathematical Physics

“…This paper is motivated by the rich applications of fractional differential equations (FDEs) in physics, economics, engineering, and many other branches of science [8,10,13,17]. Since no general method exists that can be used to analytically solve every FDE, one of the most pressing and challenging tasks is to develop suitable methods for finding analytical solutions to certain classes of FDEs [29][30][31]. Researchers have become interested in fractional interpretations of the classical integral transforms, i.e., Laplace and Fourier transforms [32][33][34], in the past few years.…”

Continuous dependence solutions for Hilfer fractional differential equations with nonlocal conditions

“…The fractional differential equations with Hilfer (generalized Riemann-Liouville) fractional derivative have recently attracted the attention of some authors interested in fractional calculus (see [1,2,9,16,20,21,25,26]). On the other hand, autonomous and non-autonomous systems of Hilfer fractional differential inclusions and equations play a considerable role that can not be over looked in the recent published researches.…”