Related papers: The tempered space-fractional Cattaneo equation
We examine the short and long-time behaviors of time-fractional diffusion equations with variable space-dependent order. More precisely, we describe the time-evolution of the solution to these equations as the time parameter goes either to…
Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We…
We begin with a brief overview of the most commonly used fractional derivatives, namely the Caputo and Riemann-Liouville derivatives. We then focus on the study of the fractional time wave equation with the Riemann-Liouville derivative,…
We analyze the fundamental solution of a time-fractional problem, establishing existence and uniqueness in an appropriate functional space. We also focus on the one-dimensional spatial setting in the case in which the time-fractional…
This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…
We study existence, uniqueness and regularity properties of classical solutions to viscous Hamilton-Jacobi equations with Caputo time-fractional derivative. Our study relies on a combination of a gradient bound for the time-fractional…
This article deals with time-fractional diffusion equations with time-dependent singular source term. Whenever the order of the time-fractional derivative is either multi-term, distributed or space-dependent, we prove that the system admits…
We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only…
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…
In this work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $\alpha\in(0,1)$. First, the well-posedness and (limited) smoothing…
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…
In this paper, we use the fractional calculus to discuss the fractional mechanics, where the time derivative is replaced with the fractional derivative of order $\nu$. We deal with the motion of a body in a resisting medium where the…
We consider an evolution equation involving the fractional powers, of order $s \in (0,1)$, of a symmetric and uniformly elliptic second order operator and Caputo fractional time derivative of order $\gamma \in (1,2]$. Since it has been…
For the fractional diffusion-wave equation with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (1,2)$ with respect to the time variable, we prove an analog of the principle of limiting amplitude (well-known for the wave…
The article provides upper bounds for the blow-up time of a system of fractional differential equations in the Caputo sense. Furthermore, concrete examples of blow-up time estimation are given using a numerical algorithm of the…
We consider the canonical fundamental systems of solutions of linear homogeneous Caputo fractional differential equations with continuous variable coefficients. Here we gained a series-representation of the canonical fundamental system by…
This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…
In the present paper, we determine the estimations on Atangana-Baleanu-Caputo fractional derivative at extreme points. With the assistance of the estimations obtained, we derive the comparison results. Peano's type existence results…
We consider a general class of integro-differential evolution equations which includes the governing equation of the generalized grey Brownian motion and the time- and space-fractional heat equation. We present a general relation between…
The ordinary subdiffusion equation, with a fractional time derivative of at most first order, describes a process in which the propagation velocity of diffusing molecules is unlimited. To avoid this non-physical property different forms of…