Final value problem for parabolic equation with fractional Laplacian and Kirchhoff's term
type: Item
instance of: scholarly article
title: Final value problem for parabolic equation with fractional Laplacian and Kirchhoff's term
zbMATH Open document ID: 1472.35437
DOI: 10.1155/2021/7238678
author: Yanyan Li
published in: Journal of Function Spaces
publication date: 2021-09-10T00:00:00Z
review text: Summary: In this paper, we study a diffusion equation of the Kirchhoff type with a conformable fractional derivative. The global existence and uniqueness of mild solutions are established. Some regularity results for the mild solution are also derived. The main tools for analysis in this paper are the Banach fixed point theory and Sobolev embeddings. In addition, to investigate the regularity, we also further study the nonwell-posed and give the regularized methods to get the correct approximate solution. With reasonable and appropriate input conditions, we can prove that the error between the regularized solution and the search solution is towards zero when \(\delta\) tends to zero.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K59
zbMATH DE Number: 7393912
zbMATH Keywords: conformable fractional derivative
zbMATH Keywords: global existence and uniqueness of mild solutions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/7238678
OpenAlex ID: W3182235278
cites work: Fractional Newton mechanics with conformable fractional derivative
cites work: Fractional conformable derivatives of Liouville-Caputo type with low-fractionality
cites work: Properties of the Katugampola fractional derivative with potential application in quantum mechanics
cites work: On well-posedness of the sub-diffusion equation with conformable derivative model
cites work: A critical analysis of the conformable derivative
cites work: Physical properties of the projectile motion using the conformable derivative
cites work: On conformable fractional calculus
cites work: Forced oscillation of fractional differential equations via conformable derivatives with damping term
cites work: Three-point boundary value problems for conformable fractional differential equations
cites work: On some new properties of fractional derivatives with Mittag-Leffler kernel
cites work: Solving PDEs of fractional order using the unified transform method
cites work: A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative
cites work: New properties of conformable derivative
cites work: New exact solutions of Burgers’ type equations with conformable derivative
cites work: Regularization of a multidimensional diffusion equation with conformable time derivative and discrete data
cites work: New anisotropic models from isotropic solutions
cites work: A discussion on the existence of positive solutions of the boundary value problems via \(\psi\)-Hilfer fractional derivative on \(b\)-metric spaces
cites work: Q3457040
cites work: Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations
cites work: Applying new fixed point theorems on fractional and ordinary differential equations
cites work: Solutions of the nonlinear integral equation and fractional differential equation using the technique of a fixed point with a numerical experiment in extended \(b\)-metric space
cites work: Existence and uniqueness results for a class of nonlocal elliptic and parabolic problems
cites work: Nonlocal \(p\)-Laplace equations depending on the \(L^p\) norm of the gradient
cites work: On Kirchhoff's Model of Parabolic Type
cites work: A new definition of fractional derivative
cites work: Semilinear conformable fractional differential equations in Banach spaces
cites work: Functional analysis, Sobolev spaces and partial differential equations
description: scientific article; zbMATH DE number 7393912