Space-dependent variable-order time-fractional wave equation: Existence and uniqueness of its weak solution

DOI10.2989/16073606.2022.2110959zbMath1521.35194OpenAlexW4295851922WikidataQ113702770 ScholiaQ113702770MaRDI QIDQ6170155

Karel Van Bockstal, Ahmed S. Hendy, Mahmoud A. Zaky

Publication date: 15 August 2023

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1854/LU-01GP0KPQRNW305VW47DXQ3TPXP

zbMATH Keywords

variable coefficientsnon-autonomous equationvariable-orderuniqueness and existencetime fractional wave equationRothe's time discretization

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Variational methods applied to PDEs (35A15) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Integro-differential operators (47G20) Fractional partial differential equations (35R11)

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Cites Work

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• Fractional Feynman-Kac equation with space-dependent anomalous exponent
• Two high-order numerical algorithms for solving the multi-term time fractional diffusion-wave equations
• On existence and uniqueness of solutions for semilinear fractional wave equations
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• A priori estimates for solutions of boundary value problems for fractional-order equations
• Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod
• Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• The variable-order fractional calculus of variations
• The Rothe method for multi-term time fractional integral diffusion equations
• Analytical solution of fractional variable order differential equations
• Variable order and distributed order fractional operators
• Solution existence for non-autonomous variable-order fractional differential equations
• Existence and uniqueness of a weak solution to a non-autonomous time-fractional diffusion equation (of distributed order)
• Existence of a unique weak solution to a non-autonomous time-fractional diffusion equation with space-dependent variable order
• A class of time-fractional hemivariational inequalities with application to frictional contact problem
• Wellposedness and regularity of a nonlinear variable-order fractional wave equation
• Regularity of solutions to space-time fractional wave equations: A PDE approach
• A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
• A semi-linear delayed diffusion-wave system with distributed order in time
• Existence and uniqueness results for Cauchy problem of variable-order fractional differential equations
• Constitutive Dynamic-Order Model for Nonlinear Contact Phenomena
• The variable viscoelasticity oscillator
• Integration and differentiation to a variable fractional order
• Applications of variable-order fractional operators: a review
• Numerical Methods for a Class of Fractional Advection-Diffusion Models with Functional Delay
• A variable order constitutive relation for viscoelasticity
• Fractional wave equation and damped waves