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261 articles for “Derivative function”
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Excerpt from the Function of a Complex Variable
Abstract: The need to derive a function arose while trying to find a universal way to determine the tangent of a curve in geometry and velocity in mechanics. In mathematical analysis, in a branch of mathematics, a derivative is a measure of how (how fast) a function changes its values when its input values change. The derivative of the curve at a point represents the coefficient of the direction of the …
Published in Research & Reviews : Journal of Statistics · Vol. 10, Issue 2, 2021 · pp. 1–7 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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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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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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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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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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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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Discrete and Continuous Indices
Abstract: Sum or integrals over discrete or continuous topological indices respectively. An analytic formalism is developed for the spectrum of discrete indices that can be completed into a continuum and continuous indices.Cite this ArticleSimon Davis. Discrete and Continuous Indices. Research & Reviews: Discrete Mathematical Structures. 2015; 2(2): 25–37p.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 2, Issue 2, 2015 · pp. 25–37 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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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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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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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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Machine Learning Based Optimization of Polymer Structure Property Relationships in Composite Material Systems
Abstract: In modern engineering applications, polymer-based composite materials have garnered a lot of attention because of their lightweight nature, high strength-to-weight ratio, and changing physical features. In order to maximize the relationships between polymer structure and properties in composite materials, this study suggests a strategy based on reinforcement learning (RL). The research utilized the Polymer Composite Properties Dataset, which contains 12,700 records associated with polymer matrices, reinforcement fillers, interfacial bonding characteristics, …
Published in Journal of Polymer & Composites · Vol. 14, Issue 3, 2026 · pp. 242–255 Read article
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Antibacterial Surfaces: A Comprehensive Review
Abstract: Microbial communities adhere to surfaces and colonize themselves. Challenges such as microbial infections are, especially, observed on the surface associated with various medical products. In this review, the authors made efforts to maintain the balance of clarity among different types of antibacterial surfaces that exhibit anti-biofouling or bactericidal or both with the help of present advancements. Besides, this review paper categorised different approaches to modify the surface to antibacterial surfaces …
Published in Journal of Polymer & Composites · Vol. 8, Issue 3, 2020 · pp. 92–99 Read article
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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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The Emerging Role of Nutraceuticals in Functional Beverages
Abstract: Nutraceuticals, derived from food sources, are gaining prominence for their potential health benefits beyond basic nutrition, often serving as remedies for chronic diseases. This includes functional beverages, such as energy drinks, sports drinks, nutraceutical drinks, and functional waters, which are formulated to provide specific health benefits, from energy enhancement to immune support. Nutraceutical beverages often contain bioactive compounds, vitamins, minerals, probiotics, herbal extracts, and adaptogens, offering a convenient way to …
Published in Research and Reviews: A Journal of Medicine · Vol. 15, Issue 1, 2025 · pp. 16–24 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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Ecological Optimization of Irreversible Carnot Magnetic Refrigerator
Abstract: Abstract An irreversible Carnot Cycle model is analyzed, with the help of various irreversibility factors, such as finite time analysis and heat leakage. In which, several important performance parameters, such as the cooling rate, coefficient of performance (COP), power input, exergy output rate, entropy generation rate, and ecological function are derived, with taking the assumptions like, heat leakage and the time of the isothermal processes in account. Ecological optimization factor …
Published in Journal of Refrigeration, Air conditioning, Heating and ventilation · Vol. 3, Issue 2, 2016 · pp. 61–68 Read article
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Optimal Simultaneous Power and Rate Adaption of Communication System over Inverse Gamma Shadowed Channels
Abstract: Adaptive capacity analysis to model various emerging wireless fields like vehicle to vehicle communication, cellular and off-body communication based on inverse gamma shadowed fading mathematical model is derived. The derived algebraic model for optimal simultaneous power and rate adaption (OPRA) is mathematically tractable in terms of numerical and analytical handling. A novel closed form model for OPRA is derived in terms of Digamma and Meijer’ s-G functions. This derived exact …
Published in Journal of Operating Systems Development & Trends · Vol. 6, Issue 1, 2019 · pp. 23–26 Read article
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A Comprehensive Review of Green Hybrid Polymer–Inorganic Composite Systems Incorporating Palm Tree Ash and Titanium Dioxide
Abstract: The increasing requests on sustainable and high performance systems have motivated extensive investigations on polymer-based hybrid systems with bio-derived and/or functional inorganic fillers. In this review, the importance of palm tree ash (PTA) and titanium dioxide (TiO₂) as synergistic fillers for polymer–inorganic hybrid composites, particularly about structure–property relations, interfacial adhesion and durability performance, is discussed. Agricultural waste-derived palm tree ash (PTA) plays as a silica-rich filler which not only aids …
Published in Journal of Polymer & Composites · Vol. 14, Issue 1, 2026 · pp. 1811–1820 Read article