Related papers: Caputo fractional stochastic differential equation…
In this work I consider the abstract Cauchy problems with Caputo fractional time derivative of order $\alpha\in(0,1]$, and discuss the continuity of the respective solutions regarding the parameter $\alpha$. I also present a study about the…
In this article, we deal with fractional stochastic differential equations, so-called Caputo type fractional backward stochastic differential equations (Caputo fBSDEs, for short), and study the well-posedness of an adapted solution to…
Using a temporally weighted norm we first establish a result on the global existence and uniqueness of solutions for Caputo fractional stochastic differential equations of order $\alpha\in(\frac{1}{2},1)$ whose coefficients satisfy a…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…
Given a fractional differential equation of order $\alpha \in (0,1]$ with Caputo derivatives, we investigate in a quantitative sense how the associated solutions depend on their respective initial conditions. Specifically, we look at two…
In this paper, we deal with a Cauchy problem for a nonlinear fractional differential equation with the Caputo derivative of order $\alpha \in (0, 1)$. As initial data, we consider a pair consisting of an initial point, which does not…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
In this paper we construct approximations for the Caputo derivative of order $1-\alpha,2-\alpha,2$ and $3-\alpha$. The approximations have weights $0.5\left((k+1)^{-\alpha}-(k-1)^{-\alpha}\right)/\Gamma(1-\alpha)$ and…
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…
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…
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…
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0, 1)$ verifying that they coincide with the same classical Stefan problem at the limit case when…
Given the Caputo-type fractional differential equation $D^\alpha y(t) = f(t, y(t))$ with $\alpha \in (1, 2)$, we consider two distinct solutions $y_1, y_2 \in C[0,T]$ to this equation subject to different sets of initial conditions. In this…
It is well known that the Leibniz rule for the integer derivative of order one does not hold for the fractional derivative case when the fractional order lies between 0 and 1. Thus it poses a great difficulty in the calculation of…
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.…
We present some distinct asymptotic properties of solutions to Caputo fractional differential equations (FDEs). First, we show that the non-trivial solutions to a FDE can not converge to the fixed points faster than $t^{-\alpha}$, where…
We study some inverse problems for time-fractional Schr\"odinger equations involving the Caputo derivative of fractional order $\alpha \in (0,1)$. We prove refined uniqueness results from sets of positive Lebesgue measure for various…
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…
Our goal is to establish a hidden regularity result for solutions of time fractional Petrovsky system where the Caputo fractional derivative is of order $\alpha\in(1,2)$. We achieve such result for a suitable class of weak solutions.