Some physical problems found in nature can follow the power law; others can follow the
Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe …

The nature is very complex to model with mathematical equations. Some physical problems
found in nature could follow the power law; other could follow the Mittag–Leffler law and …

We consider the integral and derivative operators of tempered fractional calculus, and
examine their analytic properties. We discover connections with the classical Riemann …

In this article, we first introduce an interesting new generalization of the familiar
Pochhammer symbol by means of a certain one-parameter family of generalized gamma …

Many authors have introduced and investigated certain extended fractional derivative
operators. The main object of this paper is to give an extension of the Riemann-Liouville …

In this paper, our principle aim is to establish a new extension of the Caputo fractional
derivative operator involving the generalized hypergeometric type function F p (a, b; c; z; k) …

In this paper, we present the extended Mittag-Leffler functions by using the extended Beta
functions (Chaudhry et al. in Appl. Math. Comput. 159: 589-602, 2004) and obtain some …

The purpose of this paper is to present a systematic study of some extended special
functions like B b; ρ, λ α, β x, y, 2 F 1 α, β; ρ, λ z; b and p F q α, β; ρ, λ z; b. We obtain various …

Recently, an extended operator of fractional derivative related to a generalized Beta function
was used in order to obtain some generating relations involving the extended …

In this paper, an extension of Caputo fractional derivative operator is introduced, and the
extended fractional derivatives of some elementary functions are calculated. At the same …