11 publications

• Published Subscription 23 Jun 2019

  Fractional q-Derivative and Generalized N2 Function

  By Manoj Sharma, Mohd. Farman Ali

  Abstract: AbstractThis paper is devoted to fractional q-derivative of special functions. To begin with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit and Sharma, Jain and Ali. As a special case, of fractional q-differentiation of N2 Function has been obtained.Keywords: Fractional integral and derivative operators, Fractional q-derivative, N2 Function and Special functionsMathematics Subject Classification: …

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 38–40 Read article →

• Published Subscription 21 Sep 2018

  FD and DDA of N2 Function

  By Mohd. Farman Ali, Manoj Sharma

  Abstract: The object of the present paper is to establish the results of Double Dirichlet average (DDA) of N2 Function, using Riemann-Liouville Fractional derivative (FD). This function is a modified form of Mittag-Leffler function [15]. The author drives the results between N2-function and fractional operators. The N2 Function can be measured as a Dirichlet average and connected with fractional calculus. In this paper the solution comes in compact form of double …

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 5, Issue 2, 2018 · pp. 34–39 Read article →

• Published Subscription 12 Oct 2017

  Triple Dirichlet Average of New M-Function and Fractional Derivative

  By Mohd. Farman Ali, Manoj Sharma, Renu Jain

  Abstract: Abstract:The aim of present paper to establish some results of Triple Dirichlet average of M-Function, using fractional derivative. Fractional calculus is powerful branch of mathematics that has also sporadically been applied to structural dynamics problems. Indeed, it appears to us to be a solution in search of a good problem. In that sense, it has some of the character of the laser shortly after its development. Fractional calculus is also …

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 37–41 Read article →

• Published Subscription 18 Jul 2017

  R-L-F Integral and Double Dirichlet Average of the R-Series

  By Mohd. Farman Ali

  Abstract: AbstractThe object of the present paper is to establish a result of double Dirichlet average of the R-series by using Riemann-Liouville fractional integral. The R-series can be measured as a Dirichlet average and connected with fractional calculus. In this paper, the solution comes in compact form of double Dirichlet average of R-series. The special cases of our results are same as earlier obtained by Saxena et al, for double Dirichlet …

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 1–6 Read article →

• Published Subscription 12 May 2017

  Fractional q-calculus of the R-Series

  By Mohd. Farman Ali

  Abstract: AbstractIn this present paper we introduce a new special function, called as R-series given by the author. This function is a special case of H-function given by Inayat Hussain. This paper is devoted to fractional q-derivative of special function. To begin with the theorem on term by term q-fractional differentiation has been derived. Fractional q-differentiation of R-series has been obtained. Keywords and Phrases: Fractional integral and derivative operators, Fractional q-derivative, …

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 1, 2017 · pp. 5–7 Read article →

• Published Subscription 12 May 2017

  Fractional Integral and Dirichlet Average of the R-Series

  By Mohd. Farman Ali

  Abstract: AbstractThe aim of the present paper is to investigate the results of Dirichlet average of a new special R-Series, using Riemann-Liouville Fractional derivative. The R-Series can be measured as a Dirichlet average and connected with fractional calculus. Keywords: Dirichlet average, R-series, fractional derivative, Fractional calculus operatorsCite this ArticleMohd. Farman Ali. Fractional Integral and Dirichlet Average of the R-Series. Research & Reviews: Discrete Mathematical Structures. 2017; 4(1): 1–4p.

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 1, 2017 · pp. 1–4 Read article →

• Published Subscription 1 Feb 2017

  R-L F Integral and Triple Dirichlet Average of the R-Series

  By Mohd. Farman Ali

  Abstract: AbstractIn this article, we establish the relation between some results of triple Dirichlet average of the R-series and fractional operators. We use a new special function called as R-series, which is a special case of H-function given by Inayat Hussain. In this article, the solution is obtained in compact form of triple Dirichlet average of R-series as well as conversion into single Dirichlet average of R-series, using fractional integral. Keywords: …

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 3, Issue 3, 2016 · pp. 6–12 Read article →

• Published Subscription 29 Dec 2016

  Fractional Calculus of the R-Series

  By Mohd. Farman Ali, Manoj Sharma

  Abstract: The present paper creates a special function called as R-series. This is a special case of H-function given by Inayat Hussain. The Hypergeometric function, Mainardi function and M-series follow R-series and these functions have recently found essential applications in solving problems in physics, biology, bio-science, engineering and applied science etc. Cite this ArticleMohd. Farman Ali, Manoj Sharma. Fractional calculus of the R-Series. Research & Reviews: Discrete Mathematical Structures. 2016; 3(3): …

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 3, Issue 3, 2016 · pp. 1–5 Read article →

• Published Subscription 29 Jun 2015

  Double Dirichlet Average of cosh x and Fractional Derivative

  By Mohd. Farman Ali, Renu Jain, Manoj Sharma

  Abstract: In this paper we derive the some results of Double Dirichlet average of

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 2, Issue 2, 2015 · pp. 15–20 Read article →

• Published Subscription 29 Jun 2015

  On the Fractional Calculus Operators and DefiniteResults Including N2-Function

  By Mohd. Farman Ali, Manoj Sharma, Renu Jain

  Abstract: In this present paper, fractional Riemann-Liouville calculus operators of a new special function called N2-function is introduced given by author has been obtained. This function is a modified form of Mittag-Leffler function [1]. The author drives the results between N2-function and fractional operators. Cite this Article:Mohd. Farman Ali, Manoj Sharma, Renu Jain. On the Fractional Calculus Operators and Definite Results Including N2-Function. Research & Reviews: Discrete Mathematical Structures. 2015; 2(2): …

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 2, Issue 2, 2015 · pp. 5–9 Read article →

• Published Subscription 30 Apr 2015

  Dirichlet Average of Generalization of K4: Function and Fractional Derivative

  By Mohd. Farman Ali, Manoj Sharma, Renu Jain

  Abstract: In this paper Dirichlet average of a new Special function called as generalization of K4 – function, which is recently given by Ahmad Faraj , Tariq Salim , Safaa Sadek, Jamal Ismail has been obtained. This function is an extension of R- function which is introduced by Lorenzo and Hartly (1999). This is the modification of K4 – function given by Kishan Sharma and these functions have recently found essential …

  Published in Research & Reviews: Discrete Mathematical Structures · Vol. 2, Issue 1, 2015 · pp. 20–23 Read article →