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14 publications

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    Dirichlet Average of Hyper-geometric Kiran Function and Fractional Derivative

    By Manoj Sharma, Kiran Sharma

    Abstract: Abstract: In this paper, first of all define a new function namely Hyper-geometric Kiran Function which is generalization of Hyper-geometric Function then a relation between Dirichlet average of Hyper-geometric Kiran function and fractional derivative is established.Mathematics Subject Classification: 26A33, 33A30, 33A25 and 83C99.Keywords and Phrases: Dirichlet average, Hyper-geometric Kiran function Hyper-geometric function, fractional derivative and Fractional calculus operatorsCite this Article: Manoj Sharma, Kiran Sharma. Dirichlet Average of Hyper-geometric Kiran Function …

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 3, 2019 · pp. 29–31 Read article

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    Generalized Yang-Fourier Transforms by using K-Function to Heat Conduction in a Semi-infinite Fractal Bar

    By Manoj Sharma, Kiran Sharma

    Abstract: The main objective of present research paper to solve one-dimensional fractal heat-conduction differential equation problem in a fractal semi-infinite bar has been developed by local fractional calculus employing the analytical Generalized Yang-Fourier transforms method.Keywords: Fractal bar, heat-conduction equation, Generalized Yang-Fourier transforms, Yang-Fourier transforms, local fractional calculus, K-FunctionCite this ArticleManoj Sharma, Kiran Sharma. Generalized Yang-Fourier Transforms by using K-Function to Heat Conduction in a Semi-Infinite Fractal Bar. Research & Reviews: Discrete …

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 3, 2019 · pp. 13–18 Read article

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    Fractional q-Derivative and N2 Function

    By Manoj Sharma, Mohd. Farman Ali

    Abstract: AbstractThe study of fractional q-calculus in this paper serves as a bridge between the fractional q-calculus in the literature and the fractional q-calculus of Special Functions. This paper is devoted to fractional q-derivative of special functions. Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, physics, or other applications in engineering .To begin with the theorem on …

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 41–43 Read article

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    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

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    FRACTIONAL q-DERIVATIVE AND GENERALIZED K-FUNCTION

    By Manoj Sharma, Laxmimorya ., Rajshree Mishra

    Abstract: AbstractThis investigation is basically intended to fractional q-derivative of special functions. In this article we drive the results on term by term q-fractional differentiation of a generalized k-Series. As particular case we will obtain the fractional q-differentiation of the power series and exponential series. To start 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 …

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 6, Issue 1, 2019 · pp. 6–9 Read article

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    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

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    Triple Dirichlet Average of New Generalized M-Function and Fractional Derivative

    By Manoj Sharma

    Abstract: AbstractThe aim of present work to establish some results of Triple Dirichlet average of New Generalized M-Function, using fractional derivative.Keywords and Phrases: Dirichlet average, New Generalized M-Function fractional derivative and Fractional calculus operators.Mathematics Subject Classification: 26A33, 33A30, 33A25 and 83C99. Cite this Article Manoj Sharma. Triple Dirichlet Average of New Generalized M-Function and Fractional Derivative. Research & Reviews: Discrete Mathematical Structures. 2017; 4(3): 89–93p..

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 3, 2017 · pp. 89–93 Read article

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    INTEGRAL REPRESENTATION OF K-FUNCTION

    By Manoj Sharma, Laxmi Morya, Rajshree Mishra

    Abstract: Abstract: In this article, an attempt to be made to introduce the four-different integral representation of Extended K-function and special cases have also been discussed [1, 2]. The Extended K Function which is introduced by the authors first time in this work is extended version of earlier K-Function of Sharma [3]. We will use Riemann-Liouville fractional calculus operator in finding the integral representation of this extended K- Function. Fractional Calculus …

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 3, 2017 · pp. 81–88 Read article

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    Advanced Computable Extension of New Fractional Kinetic Equation

    By Manoj Sharma, A. Tyagi

    Abstract: AbstractThe aim of this work is to find advanced computable extension of kinetic equation with fractional calculus approach. Fractional calculus originated in 1695, shortly after the inversion of classical calculus. The pioneer researchers who studied it were Liouville, Riemann, Leibniz, etc. For a long time, fractional calculus has been regarded as a pure mathematical area without applications. But, in recent decades, such type of synergism has been changed. It has …

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 3, 2017 · pp. 74–80 Read article

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    Dirichlet Average of Extended Mainardi Function and Fractional Derivative

    By Santosh Verma, Manoj Sharma

    Abstract: AbstractIn this paper, we establish a relation of Dirichlet average of Extended Mainardi function, using fractional derivative. The fractional calculus deals with integrals and derivatives of arbitrary order. Special roles in the applications of fractional calculus operators are played by the transcendental function of the Mittag-Leffler, generalized M-series function, M-function Generalized Miller-Ross function, Wright’s functions and more generally by the Meijer’s G-functions, Fox’s H-functions and Saxena’s I-function. Mathematics Subject Classification: …

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 42–45 Read article

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    Triple Dirichlet Average of M- Function and Fractional Derivative

    By Manoj Sharma, Kiran Sharma, Susheel Dhanelia

    Abstract: AbstractThe aim of present paper is to establish some results of triple Dirichlet average of function, using fractional derivative.Keywords: Dirichlet average, function fractional derivative and Fractional calculus operatorsCite this ArticleManoj Sharma,Kiran Sharma, Susheel Dhanelia. Triple Dirichlet Average of M- Function and Fractional Derivative. Research & Reviews: Discrete Mathematical Structures. 2017; 4(2): 21–25p.

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 21–25 Read article

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    Fractional Free Electron Laser Equation and K-Function

    By Manoj Sharma, Kishan Sharma

    Abstract: AbstractIn this era, fractional free electron laser (FEL) equations are studied due to their utility and importance in mathematical physics and engineering. The aim of present paper is to find the solution of generalized fractional order free electron laser (FEL) equation, using K-function. The results obtained here are moderately universal in nature. Special cases, relating to the exponential function are also considered. The special functions were introduced in 18th century …

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 17–20 Read article

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    Dirichlet Average of New Generalized M-series and Fractional Calculus

    By Manoj Sharma

    Abstract: AbstractWe know that every analytic function can be measured as a Dirichlet average and connected with fractional calculus. In this note, we set up a relation between Dirichlet average of new generalized M-series, and fractional derivative. Fractional derivative is a derivative of arbitrary order i.e. may be real, complex, integer or fractional order.Keywords: Dirichlet average new generalized M-series, fractional derivative, fractional calculus operatorsCite this ArticleManoj Sharma. Dirichlet Average of New …

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 3, Issue 3, 2016 · pp. 13–16 Read article

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    Modified Riemann−Liouville Fractional Derivative and Differential Equation for a Class of New Levy-type Probabilities

    By Mohd. Farman Ali, Manoj Sharma, Renu Jain

    Abstract: The aim of the present paper to obtained the solution of differential equations involving Modified Riemann-Liouville fractional derivative in addition to it Levy-type one sided probability density function. Some scientist studied a small number of interesting problems regarding diffusing processes in media with fractal geometry, and formulated fractional diffusion.

    Published in Research & Reviews: Discrete Mathematical Structures · Vol. 1, Issue 3, 2014 · pp. 42–44 Read article

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