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Related papers: On Stability of Generalized Cauchy-type Problem

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We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker-Planck equation, improving on previous results in several respects. Our main goal is to establish that the stability constants are bounded…

Numerical Analysis · Mathematics 2022-08-09 William McLean , Kassem Mustapha

In this paper, We study the stability of solutions of fuzzy differential equations by Lyapunov's second method. By using scale equations and comparison principle for Lyapunov - like functions, we give some sufficient criterias for the…

Dynamical Systems · Mathematics 2007-05-23 Le Van Hien

In this paper, we discuss the existence and uniqueness of solutions of a boundary value problem for a fractional differential equation of order $\alpha\in(2,3)$, involving a general form of fractional derivative. First, we prove an…

Classical Analysis and ODEs · Mathematics 2017-11-06 Ricardo Almeida

A new approach for integration of the initial value problem for ordinary differential equations is suggested. The algorithm is based on approximation of the solution by a system of functions that contains orthogonal exponential polynomials.

Numerical Analysis · Mathematics 2011-05-10 Vladimir S. Chelyshkov

This paper is devoted to the solution and stability of a one-dimensional model depicting Rao--Nakra sandwich beams, incorporating damping terms characterized by fractional derivative types within the domain, specifically a generalized…

Numerical Analysis · Mathematics 2025-05-07 Kaïs Ammari , Vilmos Komornik , Mauricio Sepúlveda , Octavio Vera

In this paper we present a new type of fractional operator, the Caputo-Katugampola derivative. The Caputo and the Caputo-Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a…

Classical Analysis and ODEs · Mathematics 2016-07-26 Ricardo Almeida , Agnieszka B. Malinowska , Tatiana Odzijewicz

This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elliptic partial differential equations and their modern…

Analysis of PDEs · Mathematics 2019-12-16 Mourad Choulli

In this paper, we discuss on the linearized stability of the trivial solution for a class of nonlinear Caputo fractional differential systems of order $\alpha\in(1,2)$. We show that some recent existing results in this direction are wrong.…

Dynamical Systems · Mathematics 2020-07-30 H. T. Tuan

Aim of this paper is to study the non-existence of global solutions of the fractional differential problem involving generalized Katugampola derivative. We utilize the test function method and fractional integration by parts formula to…

Classical Analysis and ODEs · Mathematics 2018-08-10 Sandeep P Bhairat

In this paper, we investigate the sufficient conditions for existence and uniqueness of solutions and {\delta}-Ulam-Hyers-Rassias stability of an impulsive fractional differential equation involving $\psi$-Hilfer fractional derivative.…

Classical Analysis and ODEs · Mathematics 2020-12-18 J. Vanterler da C. Sousa , Kishor D. Kucche , E. Capelas de Oliveira

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving $\Psi$-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam--Hyers…

Dynamical Systems · Mathematics 2020-12-17 Kishor D. Kucche , Jyoti P. Kharade

Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…

Dynamical Systems · Mathematics 2022-08-29 Sachin Bhalekar , Deepa Gupta

In this paper, we investigate the well-posedness and the long-time asymptotic behavior for the initial-boundary value problem for multi-term time-fractional diffusion equations, where the time differentiation consists of a finite summation…

Analysis of PDEs · Mathematics 2023-01-02 Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

The classical solvability of the initial-boundary problem for the Davey-Stewartson-II type system of equations is proved.

Analysis of PDEs · Mathematics 2007-05-23 M. M. Shakir'yanov , V. G. Volkov

We solve the Cauchy problem defined by the fractional partial differential equation $[\partial_{tt}-\kappa\mathbb{D}]u=0$, with $\mathbb{D}$ the pseudo-differential Riesz operator of first order, and the initial conditions…

Mathematical Physics · Physics 2019-07-16 Fernando Olivar-Romero , Oscar Rosas-Ortiz

We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on spatial and time variables and the zero Dirichlet boundary condition is…

Analysis of PDEs · Mathematics 2018-06-12 Adam Kubica , Masahiro Yamamoto

We prove the global strong solvability of a quasilinear initial-boundary value problem with fractional time derivative of order less than one. Such problems arise in mathematical physics in the context of anomalous diffusion and the…

Analysis of PDEs · Mathematics 2011-06-06 Rico Zacher

In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…

Dynamical Systems · Mathematics 2024-05-28 Javad A. Asadzade , Nazim I. Mahmudov

This manuscript investigates the existence and uniqueness of solutions to the first order fractional anti-periodic boundary value problem involving Caputo-Katugampola (CK) derivative. A variety of tools for analysis this paper through the…

General Mathematics · Mathematics 2019-11-21 Saleh S. Redhwan , Sadikali L. Shaikh , Mohammed S. Abdo

In this paper we develop the theory of initial and boundary value problems for the self-adjoint nabla fractional difference equation containing a Caputo fractional nabla difference that is given by \[ \nabla[p(t+1)\nabla_{a*}^\nu x(t+1)] +…

Classical Analysis and ODEs · Mathematics 2020-02-20 Kevin Ahrendt , Lydia DeWolf , Liam Mazurowski , Kelsey Mitchell , Tim Rolling , Dominic Veconi