Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, ...

Using the Wright’s generalized hypergeometric function, we investigate a class W (q, s;A,B, λ) of analytic functions with negative coefficients. We derive many results for the modified Hadamard product of functions belonging to the class W (q, s;A,B, λ). Moreover, we generalize some of the distortion theorems to the classical fractional integrals and derivatives and the Saigo (hypergeometric) o...

Given a weighted ℓ 2 space with weights associated an entire function, we consider pairs of shift operators, whose commutators are diagonal when considered as operators over general Fock space. We establish calculus for the algebra these and apply it to case Gelfond–Leontiev derivatives. This class includes many known examples, such classic fractional derivatives Dunkl operators. allows us fram...

— 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...

— 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...

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 ...

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 ...