Related papers: Initial boundary value problems for a fractional d…
The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the…
The paper considers the initial-boundary value problem for equation $D^\rho_t u(x,t)+ (-\Delta)^\sigma u(x,t)=0$, $\rho\in (0,1)$, $\sigma>0$, in an N-dimensional domain $\Omega$ with a homogeneous Dirichlet condition. The fractional…
This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and…
We improve the time decay estimates of solutions to the one-dimensional fractional diffusion equation involving the Caputo derivative. The equation is considered on the half-line. Depending on the boundary condition, we show that solutions…
In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
We introduce the notion of Caputo-Fabrizio left and right derivatives. We present sufficient conditions for the existence of symmetric positive solutions for the following Caputo-Fabrizio fractional singular integro-differential boundary…
In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximum principle well-known for the PDEs of elliptic and…
This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary…
In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary…
We prove some existence results for a class of nonlinear fractional equations driven by a nonlocal operator.
We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for…
This paper deals with the fractional Caputo--Fabrizio derivative and some basic properties related. A computation of this fractional derivative to power functions is given in terms of Mittag--Lefler functions. The inverse operator named the…
The time-fractional diffusion-wave equation is revisited, where the time derivative is of order $2 \nu$ and $0 < \nu \le 1$. The behaviour of the equation is "diffusion-like" (respectively, "wave-like") when $0 < \nu \le \frac{1}{2}$…
In this paper, we investigate direct and inverse source problems for the diffusion equation with two-term generalized fractional derivative (Hilfer derivative) in a rectangular domain. Using spectral expansion method, we derive two-term…
This paper is concerned with a class of partial differential equations, which are the linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
The present paper deals with the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally stable implicit finite difference method on quasi-uniform…