We obtain a new decomposition of the Riemann–Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class Cn, n ∈ N, and allow us to develop suitable numerical approximations with known estimations for the error. The usefulness of the obtained results, in solving fractional integral equations and fractional...

In this article, the analytical method, Homotopy perturbation method (HPM) has been successfully implemented for solving nonlinear logistic model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the method is extremely eff...

We propose an anomalous diffusion approach to analyze the electrical impedance response of electrolytic cells using time-fractional derivatives. establish, in general terms, conservation laws connected a modified displacement current entering fractional formulation Poisson–Nernst–Planck (PNP) model. In this new formalism, we obtain analytical expressions for case blocking electrodes and presenc...

Abstract. We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminaltime triplet to be optimal are obtained. Situations with constraints present at the end time are also considered. Under appropriate assumptions, it is shown that the o...

We study calculus of variations problems, where the Lagrange function depends on the Caputo-Katugampola fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo–Hadamard fractional derivatives, with dependence on a real parameter ρ. We present sufficient and necessary conditions of first and second order to determine the extremizers of a functiona...

In this paper, SIJR e-epidemic model of fractional order for the transmission of viruses in computer network with natural death has been presented. The fractional derivatives are described in the Caputo sense. In this model the nodes have two levels of infection. Predictor-Corrector method is employed to obtain numerical solution of presented model.

In this paper, we study the controllability of linear and nonlinear fractional damped dynamical systems, which involve fractional Caputo derivatives, with different order in finite dimensional spaces using the Mittag-Leffler matrix function and the iterative technique. A numerical example is provided to illustrate the theory.

This article concerns a general fractional differential equation of order between 1 and 2. We consider the cases where the nonlinear term contains or does not contain other (lower order) fractional derivatives (of RiemannLiouville type). Moreover, the nonlinearity involves also a nonlinear non-local in time term. The case where this non-local term has a singular kernel is treated as well. It is...