相关论文: A generalized Gronwall Inequality for Caputo Fract…

We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…

We deal with complex spatial diffusion equations with time-fractional derivative and study their stochastic solutions. In particular, we complexify the integral operator solution to the heat-type equation where the time derivative is…

Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…

We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variable coefficient is recovered by solving the inverse abstract…

There are numerous applications of the classical (deterministic) Gronwall inequality. Recently, Michael Scheutzow discovered a stochastic Gronwall inequality which provides upper bounds for $p$-th moments, $p\in(0,1)$, of the supremum of…

In this work we derive some inequalities for fractional boundary value problems, that generalize the well-known de la Vall\'ee Poussin inequality. With our results we also were able to improve the intervals where some Mittag-Leffler…

In this paper we explore the theory of fractional powers of non-negative (and not necessarily self-adjoint) operators and its amazing relationship with the Chebyshev polynomials of the second kind to obtain results of existence, regularity…

In this paper, a new type of the discrete fractional Gr{\"o}nwall inequality is developed, which is applied to analyze the stability and convergence of a Galerkin spectral method for a linear time-fractional subdiffusion equation. Based on…

In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…

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…

Fractional diffusion equations imply non-Gaussian distributions that generalise the standard diffusive process. Recent advances in fractional calculus lead to a class of new fractional operators defined by non-singular memory kernels,…

We begin by proving a local existence result for a fractional Caputo nonlocal thermistor problem. Then, additional existence and continuation theorems are obtained, ensuring global existence of solutions.

We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…

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…

The main contribution of this work is to construct and analyze stable and high order schemes to efficiently solve the two-dimensional time Caputo-Fabrizio fractional diffusion equation. Based on a third-order finite difference method in…

In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer difference equations with initial…

Efficient and fast predictor-corrector methods are proposed to deal with nonlinear Caputo-Fabrizio fractional differential equations, where Caputo-Fabrizio operator is a new proposed fractional derivative with a smooth kernel. The proposed…

We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…

(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…

The aim of this paper is to present a linear viscoelastic model based on Prabhakar fractional operators. In particular, we propose a modification of the classical fractional Maxwell model, in which we replace the Caputo derivative with the…