This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense of Riemman-Liouville with a Lagrangian depending on the free end-points. To illustrate our approach, two examples are discussed in detail.

Fractal and Fractional are two words referring to some characteristics and fundamental problems which arise in all fields of science and technology. These problems are characterized by having some non-integer order features. Fractals are geometrical objects with non-integer dimension, while fractional is the non-integer order of differential operators. Fractals and fractional calculus have been...

Given the recent advances regarding studies of discrete fractional calculus, and fact that dynamics discrete-time neural networks in variable-order cases have not been sufficiently documented, herein, we consider a novel class fractional-order using nabla operator variable-order. An adequate criterion for existence solution addition to its uniqueness such systems is provided with use Banach fix...

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...

A fractional-order control strategy for pneumatic position servosystem is presented in this paper. The idea of the fractional calculus application to control theorywas introduced inmanyworks, and its advantages were proved. However, the realization of fractional-order controllers for pneumatic position servosystems has not been investigated. Based on the relationship between the pressure in cyl...

Fractional calculus is about the integration or differentiation of non-integer orders. The use of “fractional” is purely due to historical reasons [1]. Using fractional order differential equations is believed to be able to better characterize the nature around us. Using an integer order model is only for our own convenience. Depending on the scale on which we characterize the dynamics of a sys...

The motion differential equation of hydro-pneumatic suspension is established to describe the vibration characteristics for a certain type construction vehicle. output force was deduced from parameters. Based on multi-phase medium, fractional calculus theory introduced, and its Bagley–Torvik formed. numerical computation by low-pass filter Oustaloup algorithm performed. solution nonlinear obtai...

In the present paper, concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo derivative. New results on existence and uniqueness are established by using theory operator semigroups, Hausdorff measure noncompactness, fixed point theorems calculus techniques. Applications a class fractional-order gene regulatory network (GRN) models propos...

The purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana-Baleanu fractional derivative. Since the new Atangana-Baleanu fractional derivative is non-singular and non-local, the Euler-Lagrange equations are proposed for the problems of Herglotz. Fractional variational Herglotz problems of variable order are considered and two cases are sho...

2. Preliminaries Fractional differintegration’s set foot in control compass, also consistency of Caputo definition among the other fractional derivative’s definitions with engineering applications, is caused to devote this section to the basic definition of fractional calculus and its properties (Table 1). The Riemann–Liouville (RL) and the Caputo are the most popular fractional derivatives def...