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The Mittag-Leffler function plays a role of central importance in the theory of fractional derivatives. In this brief note we discuss the properties of this function and its connection with the Wright-Bessel functions and with a new family…
In this paper the Mittag-Leffler function is given through the exponential functions for any rational derivatives of m/n order, where m<n, n>1 are natural irreducible numbers (if n=1 then m is also equal to unity). Unlike the previous…
Product-to-sum identities for trigonometric functions play a fundamental role in function theory and numerous applications. In this spirit, we present convolution-to-sum identities for Mittag-Leffler type functions. Using a Laplace domain…
We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired by the recent definition of spherical analyticity.
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
This paper introduces a new numerical method for approximating the Lambert W function in the real domain. The method transforms the function into a simpler form that allows iterative refinement of an initial guess. Two iterative strategies…
The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. First, by using a truncated Talbot contour…
In this paper, we develop a Multilayer (ML) method for solving one-factor parabolic equations. Our approach provides a powerful alternative to the well-known finite difference and Monte Carlo methods. We discuss various advantages of this…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
In reaction rate theory, in input-output type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their…
There is no unified method to solve the fractional differential equation. The type of derivative here used in this paper is of Jumarie formulation, for the several differential equations studied. Here we develop an algorithm to solve the…
In this paper we introduce a novel Mittag--Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or Hyper-Bessel-type operators. We discuss then the…
The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due…
We study the non-parametric estimation of the value ${\theta}(f )$ of a linear functional evaluated at an unknown density function f with support on $R_+$ based on an i.i.d. sample with multiplicative measurement errors. The proposed…
We aim to study Mittag-Leffler type functions of two variables ${{D}_{1}}\left( x,y \right),...,{{D}_{5}}\left( x,y \right)$ by analogy with the Appell hypergeometric functions of two variables. Moreover, we targeted functions…
We show that the Laplace approximation of a supremum by Lp-norms has interesting consequences in optimization. For instance, the logarithmic barrier functions (LBF) of a primal convex problem P and its dual appear naturally when using this…
Herein we propose a new numerical technique for solving field theories: the large momentum frame (LMF). This technique combines several advantages of lattice gauge theory with the simplicity of front form quantisation. We apply the LMF on…
Derivatives with respect to the parameters of the integral Mittag-Leffler function and the integral Wright function, recently introduced by us, are calculated. These derivatives can be expressed in the form of infinite sums of quotients of…
This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…
This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…