— This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the fractional embedding of differential operators and ordinary differential equations. We construct an operator combining in a symmetric way the left and right (Riemann-Liouville) fractional derivati...

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

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...

Abstract The study presented in this article involves q -calculus connected to fractional calculus applied the univalent functions theory. Riemann-Liouville integral of -hypergeometric function is defined here, and investigations are conducted using theories differential subordination superordination. Theorems corollaries containing new superordination results proved for which best dominants su...

In this paper, we consider a class of abstract Cauchy problems in the framework generalized Caputo type fractional. We discuss existence and uniqueness mild solutions to such fractional differential equations by using properties found related calculus, theory uniformly continuous semigroups operators fixed point theorem. Moreover, dependence on parameters Ulam stability solutions. At end bring ...

This paper is devoted for a rigorous investigation of Hahn’s difference operator and the associated calculus. Hahn’s difference operator generalizes both the difference operator and Jackson’s q-difference operator. Unlike these two operators, the calculus associated with Hahn’s difference operator receives no attention. In particular, its right inverse has not been constructed before. We aim to...

Several approaches to the formulation of a fractional theory calculus "variable order" have appeared in literature over years. Unfortunately, most these proposals lack rigorous mathematical framework. We consider an alternative view on problem, originally proposed by G. Scarpi early seventies, based naive modification representation Laplace domain standard kernels functions involved (constant-o...

The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It shown that the derivative integral operators are bounded. Some fundamental characteristics of new operators, such as semi-group inverse characteristics, studied. As special cases these novel several already well known in literature acquired. generalized Laplace transform evaluated. By ...

The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for functions on real positive semi-axis. main contribution of this paper is introducing a finite interval. As case Riemann–Liouville interval, we define both left- right-sided operators investigate their interconnections. results presented are 1st 2nd fundamental theorems ...