Search
18 articles for “Fractional calculus operators”
-
On the Fractional Calculus Operators and DefiniteResults Including N2-Function
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
-
Fractional Calculus of the R-Series
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
-
Dirichlet Average of Generalization of K4: Function and Fractional Derivative
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
-
INTEGRAL REPRESENTATION OF K-FUNCTION
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
-
Dirichlet Average of Extended Mainardi Function and Fractional Derivative
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
-
Fractional Integral and Dirichlet Average of the R-Series
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
-
Dirichlet Average of New Generalized M-series and Fractional Calculus
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
-
Triple Dirichlet Average of M- Function and Fractional Derivative
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
-
Dirichlet Average of Hyper-geometric Kiran Function and Fractional Derivative
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
-
Triple Dirichlet Average of New M-Function and Fractional Derivative
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
-
Triple Dirichlet Average of New Generalized M-Function and Fractional Derivative
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
-
R-L-F Integral and Double Dirichlet Average of the R-Series
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
-
Fractional q-calculus of the R-Series
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
-
FD and DDA of N2 Function
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
-
Advance Fixed Point Theorems and Its Application to Ordinary and Fractional Differential Equations
Abstract: In the present research, advanced results on the fixed point theorem are applied to typical boundary value problems. Finding a differential equation's solution under certain boundary conditions is the goal of typical boundary value topics. The article appears to extend new fixed point results to a new context, likely involving fractional operators with unique kernels, notably the Caputo-type fractional operator. This extension involves applying the fixed point theorem to a …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 1–15 Read article
-
Advanced Computable Extension of New Fractional Kinetic Equation
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
-
Fractional q-Derivative and N2 Function
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
-
Computable Extension of New Advanced Fractional Kinetic Equation
Abstract: AbstractFirst, we obtain computable extensions of advanced fractional kinetic equation. The aim of this survey is to explore the behavior of physical and biological systems from the point of view of fractional calculus. Fractional calculus, integration and differentiation of an arbitrary or fractional order, provide new tools that expand the descriptive power of calculus beyond the familiar integer-order concepts of rates of change and area under a curve. Fractional calculus …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 26–32 Read article