Related papers: Exponential quadrature rules for linear fractional…
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…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
This paper deals with initial value problems for fractional functional differential equations with bounded delay. The fractional derivative is defined in the Caputo sense. By using the Schauder fixed point theorem and the properties of the…
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…
We consider fractional differential equations of order $\alpha \in (0,1)$ for functions of one independent variable $t\in (0,\infty)$ with the Riemann-Liouville and Caputo-Dzhrbashyan fractional derivatives. A precise estimate for the order…
In order to describe more complex problem using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with…
In this work, we give the general solution sequential linear conformable fractional differential equations in the case of constant coefficients for {\alpha}(\in)(0,1]. In homogeneous case, we use a fractional exponential function which…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
We propose a Hilfer advection-diffusion equation of order $0<\alpha<1$ and type $0\leq\beta\leq1$, and find the power series solution by using variational iteration method. Power series solutions are expressed in a form that is easy to…
The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler-Lagrange type for the basic, isoperimetric, and Lagrange variational problems are…
In this paper, we first deduce the explicit formulas for the projector of the $n$th level fractional derivative and for its Laplace transform. Then the fractional relaxation equation with the $n$th level fractional derivative is discussed.…
In this paper, we develop a numerical scheme for the space-time fractional parabolic equation, i.e., an equation involving a fractional time derivative and a fractional spatial operator. Both the initial value problem and the…
The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…
In this paper, we propose a numerical scheme of the predictor-corrector type for solving nonlinear fractional initial value problems, the chosen fractional derivative is called the Atangana-Baleanu derivative defined in Caputo sense (ABC).…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By…
Derivatives of fractional order are introduced in different ways: as left-inverse of the fractional integral or by generalizing the limit of the difference quotient defining integer-order derivatives. Although the two approaches lead (under…
We construct a class of exponential type solutions for the linear, delayed heat equation. These representations may be used to provide a priori ansatzes for certain boundary and/or initial-value problems arising in heat transfer. Several of…
In this note, a numerical method based on finite differences to solve a class of nonlinear advection-diffusion fractional differential equation is proposed. The fractional operator considered here is the fractional Riemann-Liouville…
In a recent paper, Saxena et al. [1] developed the solutions of three generalized fractional kinetic equations in terms of Mittag-Leffler functions. The object of the present paper is to further derive the solution of further generalized…