Results 61 to 70 of about 612 (181)
A Review of Certain Modern Special Functions and Their Applications
Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.This review article comprehensively analyzes recent developments in the generalization of special functions (SFs) and polynomials via various fractional calculus operators (FCOs), focusing on the analytical properties and applications of extended Hurwitz–Lerch zeta, Wright, and hypergeometric functions.
Hala Abd Elmageed +2 more
wiley +1 more source
Mellin Transform of Weierstrass Zeta Function and Integral Representations of Some Lambert Series
MathematicsWe consider a series which combines two Dirichlet series constructed from the coefficients of a Laurent series and derive a general integral representation of the series as a Mellin transform.
Namhoon Kim
doaj +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.Fractional differential equations (FDEs) have received a lot of interest because of their diverse applications in engineering, mathematical physics, chemistry, and biology. This study introduces a new family of fractional integral operators using incomplete R‐function kernels, advancing the theoretical foundation of FDEs further.
Priti Purohit +4 more
wiley +1 more source
Composition Formula for Saigo Fractional q‐Calculus Operator for the q‐Analogue of the H‐Function
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.The purpose of this paper is to investigate key properties of Saigo’s fractional q‐integral and q‐derivative operators involving the q‐analogue of Fox’s H‐function. We establish four main theorems describing the action of Saigo‐type fractional q‐operators on generalised power functions expressed in terms of the q‐Fox H‐function.
Arti Sharma +3 more
wiley +1 more source
Certain Properties of Extended Mittag-Leffler-Type Function of Arbitrary Order [PDF]
مجلة جامعة النجاح للأبحاث العلوم الطبيعيةIn this paper, we introduce a new extension of Mittag-Leffler function. We investigate its basic roperties, including recurrence relations, differential formulas, integral representations, aplace transform and Mellin transform.
Maged Bin-Saad, Jihad Younis
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A Mellin Transform Approach to the Pricing of Options with Default Risk. [PDF]
Comput Econ, 2022 Choi SY, Veng S, Kim JH, Yoon JH.
europepmc +1 more source
Barrier Option Under Lévy Model : A PIDE and Mellin Transform Approach
Mathematics, 2016 We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform.
Sudip Ratan Chandra, Diganta Mukherjee
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The symmetric Mellin transform in quantum calculus
Le Matematiche, 2015 In this paper, we define the q-analogue of Mellin Transform symmetric under interchange of q and 1/q, and present some of its main properties and explore the possibility of using the integral transform to solve a class of differential equations q ...
Brahim Kamel Brahim +2 more
doaj
Mellin-Fourier series and the classical Mellin transform
Computers & Mathematics with Applications, 2000 This is a continuation of the authors' work [J. Fourier Anal. Appl. 3, No. 4, 325-376 (1997; Zbl 0885.44004)]. Starting from the finite Mellin transformation which defines the Mellin-Fourier coefficients, they carry out a direct development of the Mellin-Fourier series, quite independent of the usual Fourier theory.
Butzer, P.L., Jansche, S.
openaire +1 more source
A transformation formula with primitive character
Lietuvos Matematikos Rinkinys, 2013 We prove a transformation formula for the exponential sum involving the divisor function, and primitive character modulo q. This formula can be applied to obtain meromorphic continuation for the Mellin transform of the square of Dirichlet L-function with
Aidas Balčiūnas
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