Results 41 to 50 of about 251 (140)

Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian

Advanced Nonlinear Studies
In the present paper, we study the well-posedness of the solution to the initial boundary value problem for the damped Kirchhoff-type wave equation with fractional Laplacian.
Chen Shaohua, Han Jiangbo, Xu Runzhang, Yang Chao, Zhang Meina   +4 more
doaj   +1 more source

Ground states for fractional Schrödinger equations involving a critical nonlinearity

Advances in Nonlinear Analysis, 2016
This paper is aimed to study ground states for a class of fractional Schrödinger equations involving the critical exponents:
Zhang Xia, Zhang Binlin, Xiang Mingqi
doaj   +1 more source

Non-local gradients in bounded domains motivated by continuum mechanics: Fundamental theorem of calculus and embeddings

Advances in Nonlinear Analysis, 2023
In this article, we develop a new set of results based on a non-local gradient jointly inspired by the Riesz ss-fractional gradient and peridynamics, in the sense that its integration domain depends on a ball of radius δ>0\delta \gt 0 (horizon of ...
Bellido José Carlos, Cueto Javier, Mora-Corral Carlos   +2 more
doaj   +1 more source

A Novel Computational Technique for Numerical Approximation of Nonlinear Fractional Dynamical Systems: Convergence and Efficiency Analysis

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this work, we study a family of nonlinear fractional dynamical systems and propose a numerical procedure based on the power series iterative method (PSIM). The systems are formulated in terms of the Atangana–Baleanu–Caputo (ABC) fractional derivative, which is well‐suited to the modeling of memory and nonlocal effects.
Faten H. Damag, Amin Saif, Mohammed Alsharafi, Lakhlifa Sadek   +3 more
wiley   +1 more source

Radial symmetry, monotonicity and Liouville theorem for Marchaud fractional parabolic equations with the nonlocal Bellman operator

Advanced Nonlinear Studies
In this article, we focus on studying space-time fractional parabolic equations with the nonlocal Bellman operator and the Marchaud fractional derivative. To address the difficulty caused by the space-time non-locality of operator ∂tα−Fs ${\partial }_{t}^
Liu Mengru, Zhang Lihong, Wang Guotao
doaj   +1 more source

Hardy–Hilbert Inequalities in Weighted Morrey Spaces: Commutators and Applications to Fractional PDEs on Bounded Domains for Financial Analysis

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we develop Hardy–Hilbert‐type integral estimates in weighted Morrey spaces on bounded domains and study the associated commutators with BMO symbols. The analysis is positioned relative to existing weighted Morrey estimates for fractional and rough operators, and the hypotheses needed for the fractional‐integral reduction are stated ...
Philip Ajibola Bankole, Mohsin Nasir, Sina Etemad, Smritijit Sen   +3 more
wiley   +1 more source

Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator

Advances in Nonlinear Analysis
In this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_ ...
Yang Zerong, He Yong
doaj   +1 more source

Fractional Hardy-Sobolev equations with nonhomogeneous terms

Advances in Nonlinear Analysis, 2021
This paper deals with existence and multiplicity of positive solutions to the following class of nonlocal equations with critical nonlinearity:
Bhakta Mousomi, Chakraborty Souptik, Pucci Patrizia   +2 more
doaj   +1 more source

Blow‐Up Criteria for Higher Order Fractional Moore–Gibson–Thompson Equations With Fractional Laplacian Damping

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper presents the first systematic analysis of critical exponents for both third and fourth‐order fractional Moore–Gibson–Thompson (MGT) equations with combined spatiotemporal fractional derivatives and structural damping. We establish sharp nonexistence results for global solutions via an adapted test function method, deriving explicit critical ...
Ahlem Merah, Hussien Albala, Fares Yazid, Hicham Saber, Mohammed Almalahi, Abdelkader Moumen, Khaled Aldwoah, Smritijit Sen   +7 more
wiley   +1 more source

A Poster about the Old History of Fractional Calculus [PDF]

, 2010
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010.
J. T. MACHADO, V. KIRYAKOVA, Kiryakova, Virginia, Tenreiro Machado, J., Tenreiro Machado, J. A., Mainardi, Francesco   +5 more
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