Here we derive a multivariate fractional representation formula involving ordinary partial derivatives of …rst order. Then we prove a related multivariate fractional Ostrowski type inequality with respect to uniform norm. 2010 AMS Mathematics Subject Classi…cation : 26A33, 26D10, 26D15.

In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, ...

Here we derive multivariate weighted fractional representation formulae involving ordinary partial derivatives of …rst order. Then we present related multivariate weighted fractional Ostrowski type inequalities with respect to uniform norm. 2010 AMS Mathematics Subject Classi…cation : 26A33, 26D10, 26D15.

We prove a second Noether theorem for Lagrangian densities with fractional derivatives defined in the Riesz–Caputo sense. An application to the fractional electromagnetic field is given. AMS Subject Classifications: 49K05, 26A33.

This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method proposed by Suarez and Shokooh is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duha...

In this paper we use the fuzzy Caputo derivatives under generalized Hukuhara difference to introduce fuzzy fractional Volterra-Fredholm integro-differential equations and prove the existence and uniqueness of the solutions for this class of fractional equations.

We prove a Noether’s theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.

In the paper under review, we analyze a class of abstract distributionally chaotic (multi-term) fractional differential equations in Banach spaces, associated with use of the Caputo fractional derivatives. AMS Mathematics Subject Classification (2010): 47A16, 47D03, 47D06, 47D99

Evolution equations for anomalous diffusion employ fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. This paper develops the mathematical foundations of those operators.