This paper is based upon incomplete fractional calculus and with the help of this, derived fractionalcalculus formula for Mittag-Leffler function. The results obtained are found in form ofincomplete Wright function hypergeometric

For nonlinear systems affine in the input with state x ∈ R, input u ∈ R and output y ∈ R, it is a well-known fact that, if the function mapping (x, u, . . . , u(n−1)) into (u, . . . , u(n−1), y, . . . , y(n−1)) is an injective immersion, then the system can be locally transformed into an observability normal form with a triangular structure appropriate for a high-gain observer. In this technica...

We derive asymptotic bounds for the ordinary generating functions of several classical arithmetic functions, including the Möbius, Liouville, and von Mangoldt functions. The estimates result from the KorobovVinogradov zero-free region for the Riemann zeta-function, and are sharper than those obtained by Abelian theorems from bounds for the summatory functions. Such functions as P μ(n)x, P φ(n)x...

This paper presents a model of a debit or credit card payment scheme, providing a simple determination of the socially optimal structure of fees between those charged to cardholders and those charged to merchants.  2003 Elsevier B.V. All rights reserved.

Abstract We compute asymptotic estimates for the Fourier coefficients of two mock theta functions, which come from Bailey pairs derived by Lovejoy and Osburn. To do so, we employ circle method due to Wright a modified Tauberian theorem. encounter cancelation in our one functions auxiliary function $$\theta _{n,p}$$ θ</...

Given a function ψ in L2(Rd), the affine (wavelet) system generated by ψ, associated to an invertible matrix a and a lattice Γ, is the collection of functions {| det a|j/2ψ(ajx−γ) : j ∈ Z, γ ∈ Γ}. In this article we prove that the set of functions generating affine systems that are a Riesz basis of L2(Rd) is dense in L2(Rd). We also prove that a stronger result is true for affine systems that a...

Due to rigorous work on integral operators and the hypergeomet-ric functions, we define here an integral operator involving generalized hypergeometric function. By means of this generalized function, we introduce new classes of analytic functions and study their properties. 1 Introduction and preliminaries. Let H be the class of functions analytic in U := {z ∈ C : |z| < 1} and A be the subclass...

Abstract We prove the finiteness of formal analogs spherical function (Spherical Finiteness), ${\textbf c}$-function (Gindikin–Karpelevich and obtain a analog Harish-Chandra’s limit (Approximation Theorem) relating in setting $p$-adic Kac–Moody groups. The theorems imply that Gindikin–Karpelevich integral is well defined local settings. These results extend Braverman–Garland–Kazhdan–Patnaik’s a...

Let (Ω,F,P) be a probability space and L0(F) the algebra of equivalence classes real-valued random variables defined on (Ω,F,P). A left module M over (briefly, an L0(F)-module) is said to regular if x=y for any given two elements x y in such that there exists countable partition {An,n∈N} Ω F I˜An⋅x=I˜An⋅y each n∈N, where IAn characteristic function An I˜An its class. The purpose this paper esta...