fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order.the purpose of this work is to use hadamard fractional integral to establish some new integral inequalities of gruss type by using one or two parameters which ensues four main results . furthermore, other integral inequalities of reverse m...

ABSTRACT In this paper, we employ the generalized fractional calculus operators on the generalized Mittag-Leffler function. Some results associated with generalized Wright function are obtained. Recent results of Chaurasia and Pandey are obtained as special cases. 2000 MATHEMATICS SUBJECT CLASSIFICATION 33C45, 47G20, 26A33.

In economics, depreciation functions (operator kernels) are certain decreasing functions, which assumed to be equal unity at zero. Usually, an exponential function is used as a function. However, in operator kernels do not allow simultaneous consideration of memory effects and effects. this paper, it proposed consider non-exponential type, simultaneously take into account by using the Prabhakar...

In this article, we extend fractional operators with nonsingular Mittag-Leffler kernels, a study initiated recently by Atangana and Baleanu, from order [Formula: see text] to higher arbitrary order and we formulate their correspondent integral operators. We prove existence and uniqueness theorems for the Caputo ([Formula: see text]) and Riemann ([Formula: see text]) type initial value problems ...

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

Making use of a differential operator the author investigate the various impartant properties and characteristics of the subclass Tj(n,m, p, q, α) (p, j,m ∈ N = {1, 2, . . .}, q, n ∈ N0 = N ∪ {0}, 0 ≤ α < p − q) of p-valently analytic functions with negative coefficients. Finally, several applications involving an integral operator and certain fractional calculus operators are also considered.

In this survey we present a brief history and the basic ideas of the generalized fractional calculus (GFC). The notion “generalized operator of fractional integration” appeared in the papers of the jubilarian Prof. S.L. Kalla in the years 1969-1979 when he suggested the general form of these operators and studied examples of them whose kernels were special functions as the Gauss and generalized...

Abstract We know that interpolation spaces in terms of analytic semigroup have a significant role into the study strict Hölder regularity solutions classical abstract Cauchy problem (ACP). In this paper, we first construct solution operators fractional calculus and characterize these spaces. Then establish mild order ACP.

Although many mathematicians have searched on the fractional calculus since many years ago, but its application in engineering, especially in modeling and control, does not have many antecedents. Since there are much freedom in choosing the order of differentiator and integrator in fractional calculus, it is possible to model the physical systems accurately. This paper deals with time-domain id...