Author
Suman Goyal
Other affiliations: University of Rajasthan, Banasthali Vidyapith, Malaviya Regional Engineering College ...read more
Bio: Suman Goyal is an academic researcher from India Meteorological Department. The author has contributed to research in topics: Analytic function & Fractional calculus. The author has an hindex of 11, co-authored 49 publications receiving 873 citations. Previous affiliations of Suman Goyal include University of Rajasthan & Banasthali Vidyapith.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the second and third Maclaurin coefficients of certain bi-univalent functions in the open unit disk defined by convolution are determined, and some special cases are also indicated.
48 citations
TL;DR: In this article, the authors considered sufficient conditions for analytic functions in the open unit disk to be starlike and established three theorems by using Jack's lemma and a simple result contained in Lemma 2.2.
Abstract: The purpose of the present paper is to consider some sufficient conditions for analytic functions in the open unit disk to be starlike. Here we establish three theorems by using Jack's lemma and a simple result contained in Lemma 2.2. Our theorems provide improvements of the results about sufficient conditions for starlike functions given earlier by Lewandowski et al. (2), Li and Owa (3), Nunokawa et al. (5) and Ramesha et al. (6).
38 citations
TL;DR: In this paper, Srivastava-Attiya operator is used to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk U.
Abstract: Srivastava-Attiya operator is used to define some new subclasses of strongly starlike and strongly convex functions of order β and type α in the open unit disk U. For each of these new function classes, several inclusion relationships are established. Some interesting corollaries and applications of the results presented here are also discussed.
35 citations
TL;DR: A majorization problem involving starlike function of complex order belonging to a certain class defined by means of fractional derivatives is investigated.
33 citations
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TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
7,412 citations
TL;DR: Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes as mentioned in this paper, and a large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker-Planck equation.
Abstract: Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes. A large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker–Planck equation (Metzler R and Klafter J 2000a, Phys. Rep. 339 1–77). It therefore appears timely to put these new works in a cohesive perspective. In this review we cover both the theoretical modelling of sub- and superdiffusive processes, placing emphasis on superdiffusion, and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function. We also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems.
2,119 citations
TL;DR: A survey of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date can be found in this article, where the authors report some of the most important documents and major events.
1,267 citations
TL;DR: In this article, the Green's function of fractional diffusion is shown to be a probability density and the corresponding Green's functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited.
Abstract: Diffusion and wave equations together with appropriate initial condition(s) are rewritten as integrodifferential equations with time derivatives replaced by convolution with tα−1/Γ(α), α=1,2, respectively. Fractional diffusion and wave equations are obtained by letting α vary in (0,1) and (1,2), respectively. The corresponding Green’s functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited. In particular, it is shown that the Green’s function of fractional diffusion is a probability density.
1,046 citations
01 Jan 2014
TL;DR: In this paper, Dzherbashian [Dzh60] defined a function with positive α 1 > 0, α 2 > 0 and real α 1, β 2, β 3, β 4, β 5, β 6, β 7, β 8, β 9, β 10, β 11, β 12, β 13, β 14, β 15, β 16, β 17, β 18, β 20, β 21, β 22, β 24
Abstract: Consider the function defined for \(\alpha _{1},\ \alpha _{2} \in \mathbb{R}\) (α 1 2 +α 2 2 ≠ 0) and \(\beta _{1},\beta _{2} \in \mathbb{C}\) by the series
$$\displaystyle{ E_{\alpha _{1},\beta _{1};\alpha _{2},\beta _{2}}(z) \equiv \sum _{k=0}^{\infty } \frac{z^{k}} {\varGamma (\alpha _{1}k +\beta _{1})\varGamma (\alpha _{2}k +\beta _{2})}\ \ (z \in \mathbb{C}). }$$
(6.1.1)
Such a function with positive α 1 > 0, α 2 > 0 and real \(\beta _{1},\beta _{2} \in \mathbb{R}\) was introduced by Dzherbashian [Dzh60].
919 citations