[PDF] Top 20 Autoconvolution equations and generalized Mittag-Leffler ‎functions

... the generalized Mittag- Leffler function especially in the theory of frac- tional calculus and detect some of their appli- cations in the physics and ...of generalized fractional derivatives ... See full document

... Mittag-Leffler functions play a vital role in determining the solutions of fractional differ- ential and integral equations which are associated with an extensive variety of problems in diverse areas of ... See full document

... the Mittag-Leffler function plays fundamental roles in applications of frac- tional calculus like fractional relaxation and fractional oscillation ...multi-index Mittag-Leffler functions as their typical ... See full document

... [5] R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, in: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer ... See full document

... of Mittag-Leffler functions. The Mittag-Leffler type functions have widespread applications in physics, biology, chem- istry, engineering, and some other applied ...these functions can be ... See full document

... Mittag-Leffler functions are important in studying solutions of fractional differential equa- tions, and they are associated with a wide range of problems in many areas of mathematics and ...of ... See full document

... involving generalized Galu e′ type Struve function in terms of Fox-Wright ...the generalized Galu e ′ type Struve function has a close relationship with some known special functions such as Struve ... See full document

... Kiryakova, Multiple (multiondex) Mittag-Leffler functions and relations to generalized frac- tional calculus, Journal of Computational and Applied Mathematics , 118(2000), 241-259. [11] [r] ... See full document

... Below we investigate the corresponding Euler–Lagrange equations for a Lagrangian pos- sessing the left new Caputo derivative with three parameter Mittag-Leffler kernel. Theorem 6 Let 0 < α ≤ 1, μ > 0, γ ... See full document

... The Mittag-Leffler function plays an important role in several branches of mathematics and engineering sciences, such as statistics, chem- istry, mechanics, quantum physics, informatics and ...of Mittag-Leffler ... See full document

... The function Aleph of several variables generalizes the multivariable I-function recently studied by C.K. Sharma and Ahmad [5] , itself is a generalisation of G and H-functions of multiple variables. The multiple ... See full document

... In this paper we have derived the Laplace transform and the Mellin transform and various properties of the operator defined by (). These properties are useful in solving applied problems of science, engineering and ... See full document

... The fractional calculus started to be investigated deeply in both theorical and applied view points. One of the main reasons of the fast development of this type of calculus is that it incorporates, as a particular case, ... See full document

... Fractional nabla calculus is a new branch of mathematics which deals with arbitrary order sums and differences and their properties in nabla perspective. The concept of fractional nabla difference dates back to the works ... See full document

... The Mittag-Leffler function has gained importance and popularity during the last one and a half decades due mainly to its applications in the solution of fractional-order differential, integral and ... See full document

... the Mittag-Leffler ...This Mittag-Leffler function distribution (MLFD) belongs to the generalized hypergeometric and generalized power series families and also arises as weighted ... See full document

... The Mittag-Leffler function and its generalizations used to obtain a new method for solving system of nonlinear fractional differential equations (Lorenz ... See full document

... In a number of subsequent works including [], the k-gamma function and k-Pochhammer symbol have been used to extend and investigate such special func- tions and integral operators as (for example) the k-beta function, ... See full document

... a generalized multiple-index Mittag-Leffler function,hyperbolic functions, multivariable Aleph-function, the multivariable I-function defined by Prasad [4] and general class of polynomials of ... See full document

...  associated with a general class of polynomials. The integral obtained is unified in nature and act as key formula from which we can obtain as their special cases, integral formulae concerning a large number of simpler ... See full document