Analysis of fractional integro-differential equations of thermistor type
Abstract
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional integral and differential equations of thermistor type. Several nonlocal problems are considered: with Riemann-Liouville, Caputo, and time-scale fractional operators. Existence and uniqueness of positive solutions are obtained through suitable fixed-point theorems in proper Banach spaces. Additionally, existence and continuation theorems are given, ensuring global existence.
Keywords
Cite
@article{arxiv.1807.01529,
title = {Analysis of fractional integro-differential equations of thermistor type},
author = {Moulay Rchid Sidi Ammi and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1807.01529},
year = {2018}
}
Comments
This is a preprint of a paper whose final and definite form is in 'Handbook of Fractional Calculus with Applications. Vol 1: Basic Theory', De Gruyter. Submitted 28/March/2018; revised 03/May, 04/May and 04/July/2018; accepted 04/July/2018