相关论文: Generalization of the final-value theorem and its …

In this paper, we present a new derivative via the Laplace transform. The Laplace transform leads to a natural form of the fractional derivative which is equivalent to a Riemann-Liouville derivative with fixed terminal point. We first…

We generalize the classical mean value theorem of differential calculus by allowing the use of a Caputo-type fractional derivative instead of the commonly used first-order derivative. Similarly, we generalize the classical mean value…

We consider the terminal value problem (or called final value problem, initial inverse problem, backward in time problem) of determining the initial value, in a general class of time-fractional wave equations with Caputo derivative, from a…

In this work, we consider a generalization of the nonlinear Langevin equation of fractional orders with boundary value conditions. The existence and uniqueness of solutions are studied by using results of the fixed point theory. Moreover,…

In the paper, we considered the existence and uniqueness of the global solution in the space of continuously differentiable functions for a nonlinear differential equation with the Caputo fractional derivative of general form. Our main…

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…

Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the…

The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…

We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…

Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed…

An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…

We discuss the existence, non-existence and multiplicity of nontrivial solutions for systems of Caputo fractional differential equations subject to nonlocal boundary conditions. Our methodology relies on classical fixed point index and we…

In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our…

In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain $D$ of $ \mathbb{R}^{k}$, $k\ge 1$, which includes the fractional power $\mathcal L^\beta$, $0<\beta\le…

In this paper we obtain new estimates of the sequential Caputo fractional derivatives of a function at its extremum points. We derive comparison principles for the linear fractional differential equations, and apply these principles to…

In this paper strong dissipativity of generalized time-fractional derivatives on Gelfand triples of properly in time weighted $L^p$-path spaces is proved. In particular, the classical Caputo derivative is included as a special case. As a…

In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work \cite{fllx17}. Here we use the definition of Caputo derivative proposed in \cite{liliu17frac1,liliu2017}…

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…

In this research work, let us focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave…

We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated…