R.K. SAXENA Department of Mathematics and Statistics, Jai Narain Vyas University Jodhpur 342001, INDIA A.M. MATHAI Department of Mathematics and Statistics, McGill University, 805 Sherbooke Street West, Montreal, CANADA H3A 2K6 H.J. HAUBOLD Office for Outer Space Affairs, United Nations, P.O. Box 500, A-1400 Vienna, AUSTRIA Abstract. The subject of this paper is to derive the solution of genera...

The aim of this paper is to study some properties of multiindex Mittag-Leffler type function E(1/ρj),(μj)(z) introduced by Kiryakova [V. Kiryakova, J. Comput. Appl. Math. 118 (2000), 241-259]. Here we establish certain theorems which provide the image of this function under the Saigo’s fractional integral operators. The results derived are of general character and give rise to a number of known...

In this paper, we derive the representation formula of solution for ?-Hilfer fractional differential equation with constant coefficient in form Mittag-Leffler function by using Picard’s successive approximation. Moreover, some properties and fixed point theorems such as Banach Schaefer, introduce new results qualitative existence uniqueness. The generalized Gronwall inequality lemma is used ana...

In the current paper, we consider multi-derivative nonlinear fractional differential equations involving Atangana-Baleanu derivative. We investigate fundamental results about existence, uniqueness, boundedness and dependence of solution on various data. The analysis is based a integral operator due to T. R. Prabhakar generalized Mittag-Leffler function, Krasnoselskii’s fixed point theorem Gronw...

In this work, the newly developed optimal perturbation iteration technique with Laplace transform is applied to generalized regularized long wave equations a new fractional operator obtain approximate solutions. We classical differential form by using Atangana-Baleanu derivative which defined Mittag-Leffler function. To show efficiency of proposed method, numerical example given for different v...

Various extensions of classical gamma, beta, Gauss hypergeometric and confluent functions have been proposed recently by many researchers. In this paper, we further generalized extended beta function with some its properties such as symmetric properties, summation formulas, integral representations, connection other special error, Mittag – Leffler, incomplete hypergeometric, Wright, Fox H Meije...

The objective of this paper is to investigate natural transform Meijer’s G-Function in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties terms Mittag-Leffler functions. Further, we show some applications these classical equations mathematical physics, like the heat free electron laser equations, difference-differential gove...