Related papers: An analytic semigroup generated by a fractional di…

The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fractional differential equations with the Caputo derivatives, the…

We study a space-fractional Stefan problem, where the non-local diffusion flux is modeled by the Caputo derivative. We obtain the unique existence of classical solution to this problem.

We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only…

We consider five different abstract Cauchy problems where the operator is of fourth order. For each problem, using semigroups techniques and functional calculus, we study the invertibility and the spectral properties of the fourth order…

Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart hyper-Bessel operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansion…

This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…

In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputo-type differential operator proposed by Kochubei. First, the existence, the positivity and the long time behavior of…

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor's Theorem,…

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…

There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related…

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties.…

We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…

We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…

We derive a fundamental solution $\mathscr{E}$ to a space-fractional diffusion problem on the half-line. The equation involves the Caputo derivative. We establish properties of $\mathscr{E}$ as well as formulas for solutions to the…

This paper is devoted to describing a linear diffusion problem involving fractional-in-time derivatives and self-adjoint integro-differential space operators posed in bounded domains. One main concern of our paper is to deal with singular…

We establish partial semigroup property of Riemann-Liouville and Caputo fractional differential operators. Using this result we prove theorems on reduction of multi-term fractional differential systems to single-term and multi-order…

The fractional calculus is useful to model non-local phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution…

An autonomous Caputo fractional differential equation of order $\alpha\in(0,1)$ in $\mathbb{R}^d$ whose vector field satisfies a global Lipschitz condition is shown to generate a semi-dynamical system in the function space $\mathfrak{C}$ of…

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,…

In this paper, we focus on a space-time fractional diffusion equation with the generalized Caputo's fractional derivative operator and a general space nonlocal operator (with the fractional Laplace operator as a special case). A weak…