Optimal control of a nonlocal thermistor problem with ABC fractional time derivatives

DOI10.1016/j.camwa.2019.03.043zbMath1442.49027arXiv1903.07961OpenAlexW2921230553WikidataQ128141177 ScholiaQ128141177MaRDI QIDQ2203210

Moulay Rchid Sidi Ammi, Delfim F. M. Torres

Publication date: 5 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.07961

zbMATH Keywords

optimal controlexistence of solutionsfractional partial differential equationsABC fractional derivatives

Mathematics Subject Classification ID

Foundations of thermodynamics and heat transfer (80A05) Optimality conditions for problems involving relations other than differential equations (49K21) Fractional partial differential equations (35R11) Existence theories for optimal control problems involving relations other than differential equations (49J21)

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Cites Work

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• Numerical solutions of the thermistor equations
• Existence of a solution to the Stefan problem with Joule's heating
• The extended fractional Caputo-Fabrizio derivative of order \(0\leq \sigma <1\) on \(C_{\mathbb{R}}[0,1\) and the existence of solutions for two higher-order series-type differential equations]
• Fractional derivatives with no-index law property: application to chaos and statistics
• Non validity of index law in fractional calculus: a fractional differential operator with Markovian and non-Markovian properties
• Necessary optimality conditions for a dead oil isotherm optimal control problem
• Remarks on the existence, uniqueness and semi-explicit solvability of systems of autonomous partial differential equations in divergence form with constant boundary conditions
• Optimal Control of a Convective Boundary Condition in a Thermistor Problem
• Numerical Solution of a Non-Local Elliptic Problem Modeling a Thermistor with a Finite Element and a Finite Volume Method
• Temperature Surges in Current-Limiting Circuit Devices
• Numerical Computation of a Fractional Derivative with Non-Local and Non-Singular Kernel
• Basic Theory
• Thermal runaway in a non-local problem modelling Ohmic heating. Part II: General proof of blow-up and asymptotics of runaway
• Optimal control of nonlocal thermistor equations
• Analysis of Optimal Control Problems for the Two-Dimensional Thermistor System
• Optimal control theory for ambient pollution
• Optimal control for the thermistor problem with a current limiting device

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