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Title: Analysis of fractional integro-differential equations of thermistor type
Author: Sidi Ammi, Moulay Rchid
Torres, Delfim F. M.
Keywords: Integral and differential equations
Fractional operators
Nonlocal thermistor problems
Time scales
Dynamic equations
Positive solutions
Local and global existence
Fixed-point theorems
Issue Date: 2019
Publisher: De Gruyter
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 as regards fractional integral and differential equations of thermistor type. Several nonlocal problems are considered: problems concerned with Riemann–Liouville, Caputo, and time-scale fractional operators. The 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.
Peer review: yes
DOI: 10.1515/9783110571622-013
ISBN: 978-3-11-057162-2
Publisher Version:
Appears in Collections:CIDMA - Capítulo de livro
SCG - Capítulo de livro

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