Related papers: Van der Corput lemmas for Mittag-Leffler functions…

We develop a new generalized form of the fractional kinetic equation involving a generalized k-Bessel function. The generalized $k$-Mittag-leffler function $E^{\gamma,q}_{k,\alpha,\beta}(.)$ is discussed in terms of the solution of the…

Integral representations play a prominent role in the analysis of entire functions. The representations of generalized Mittag-Leffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in…

In this article, we introduce Mittag-Leffler L\'evy process and provide two alternative representations of this process. First, in terms of Laplace transform of the marginal densities and next as a subordinated stochastic process. Both…

In this paper, we consider Caputo type fractional stochastic time-delay system with permutable matrices. We derive stochastic analogue of variation of constants formula via a newly defined delayed Mittag-Leffer type matrix function. Thus,…

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…

We generalize the Bartsch-Li's splitting lemma at infinity for $C^2$-functionals in [2] and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow…

We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the $L^s$-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and…

We study the generalized fractional linear problem $D^{\nu}_{a+*} f(x) =A(x)f(x)+g(x)$, where $D^{\nu}$ is an arbitrary mixture of Caputo derivatives of order at most one and $A(x)$ a family of operators in a Banach space generating…

We study Mittag-Leffler conditions on modules providing relative versions of classical results by Raynaud and Gruson. We then apply our investigations to several contexts. First of all, we give a new argument for solving the Baer splitting…

We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.

In this paper we study linear and nonlinear fractional differential equations involving the Caputo fractional derivative with Mittag-Leffler non-singular kernel of order $0<\alpha<1.$ We first obtain a new estimate of the fractional…

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…

The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamiltonian is found to be non-Hermitian and non-local in time.…

We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and…

We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…

This paper is in concern with Cauchy problems involving the fractional derivatives with respect to another function. Results of existence, uniqueness, and Taylor series among others are established in appropriate functional spaces. We prove…

Linear differential equations with variable coefficients and Prabhakar-type operators featuring Mittag-Leffler kernels are solved. In each case, the unique solution is constructed explicitly as a convergent infinite series involving…

Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…

We consider a class of diffusion equations with the Caputo time-fractional derivative $\partial_t^\alpha u=L u$ subject to the homogeneous Dirichlet boundary conditions. Here, we consider a fractional order $0<\alpha < 1$ and a second-order…

This paper presents the Euler-Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses…