Research & Reviews: Discrete Mathematical Structures
Volume 4, Issue 2 (2017)
Published
Table of contents
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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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Fractional Free Electron Laser Equation and K-Function
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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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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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
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Integral of Generalized M-Function Involving Product of Special Functions
Abstract: AbstractIn this paper, an attempt to be made for study about integrals of generalized M-Function multiplied with Jacobi polynomial.Keywords: Generalized Mittag-Leffler function, Generalized M-Function.Cite this ArticleLaxmi Morya, Manoj Sharma, Rajshree Mishra. Integral of Generalized M-Function Involving Product of Special Functions. Research & Reviews: Discrete Mathematical Structures. 2017; 4(2): 33–36p.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 33–36 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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Asymptotically Double Lacunary Equivalent Sequences Defined by Ideals and Orlicz Functions
Abstract: AbstractIn the present manuscript, we are going to introduce some new definitions that are a generalization of those given by Esi in 2014 about asymptotically equivalent and Orlicz function with respect to an ideal. We established some sequence spaces and studied some inclusion relations about them. The results obtained in this study are more than those obtained by Esi in 2009 and 2014.Keywords: Pringsheim limit, Orlicz functions, equivalent sequencesCite this …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 7–16 Read article