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46 articles for “fractional derivative”
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Modified Riemann−Liouville Fractional Derivative and Differential Equation for a Class of New Levy-type Probabilities
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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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
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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
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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
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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
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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
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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
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Double Dirichlet Average of cosh x and Fractional Derivative
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
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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
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Fractional q-Derivative and Generalized N2 Function
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
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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Review on Fractional Order Sliding Mode Control of Nonlinear System
Abstract: This paper presents review fractional order sliding mode control of nonlinear system.Sliding mode control (SMC) may be a variable structure control (VSC). It is a nonlinear manipulates approach that approaches in supplied,an impact action andrestricts plant to manage to feature in accordance to some pre-defined ordinary dynamic. This desired dynamic is mentioned as sliding surface. When plant follows sliding surface, it is in sliding mode.Fractional sliding mode control (FSMC) is …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 8, Issue 1, 2021 · pp. 8–16 Read article
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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
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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
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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
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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
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Modelling of The Viscoelastic Composite Curved Panel for The Time Domain Analysis Using TTBDF, β1 / β2−Bathe and Newmark Method
Abstract: Viscoelastic materials are extensively used in structures, especially thin-walled structures, for damping. The accurate modelling of the time domain dynamics of the viscoelastic material is essential for appropriately capturing the damping of the viscoelastic material. Various implicit and explicit time integration schemes are available to evaluate time domain response. However, the rightness of the implementation of the time integration scheme to the viscoelastic material model is very essential. In this …
Published in Journal of Polymer & Composites · Vol. 13, Issue 1, 2025 · pp. 204–222 Read article
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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
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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
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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