Pathway fractional integral operator and matrix-variate functions

Nair, Seema S.

doi:10.1080/10652469.2010.511211

Cited by 6 publications

(8 citation statements)

References 10 publications

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“…Corollary 2.6. If we put τ = q = 1, ν = σ = p = ζ = k = 1 in Theorem 2.4, then it reduces to the following result of Nair [17].…”

Section: Now Interchanging the Inner Integral By Beta Function Formula We Getmentioning

confidence: 94%

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The pathway integral operator involving extension of k-Bessel-Maitland function

Ahmad¹,

Porwal²

2021

Maltepe Journal of Mathematics

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“…Corollary 2.6. If we put τ = q = 1, ν = σ = p = ζ = k = 1 in Theorem 2.4, then it reduces to the following result of Nair [17].…”

Section: Now Interchanging the Inner Integral By Beta Function Formula We Getmentioning

confidence: 94%

“…Recently, by using the pathway idea of Mathai [13] and developed further by Mathai and Haubold [14,15], Nair [17], we introduce a pathway fractional integral operator which is given below.…”

Section: Introductionmentioning

confidence: 99%

The pathway integral operator involving extension of k-Bessel-Maitland function

Ahmad¹,

Porwal²

2021

Maltepe Journal of Mathematics

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“…In particular, for β = 1 and ρ = 1, the integral of Equation (19) can be treated as the pathway fractional integral transform of the Mittag-Leffler function with appropriate transformation of the variable. More details about pathway fractional integral transform can be found in Seema Nair ((2009) [8], (2011) [9]). The model in Equation 15can be connected to the superstatistics of Beck and Cohen (2003) [10] and Beck (2006) [11] for q = 2, δ = 0.…”

Section: The Q-analogue Of Generalized Gamma Mittag-leffler Densitymentioning

confidence: 99%

An Overview of Generalized Gamma Mittag–Leffler Model and Its Applications

Nair

2015

Axioms

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Recently, probability models with thicker or thinner tails have gained more importance among statisticians and physicists because of their vast applications in random walks, Lévi flights, financial modeling, etc. In this connection, we introduce here a new family of generalized probability distributions associated with the Mittag-Leffler function. This family gives an extension to the generalized gamma family, opens up a vast area of potential applications and establishes connections to the topics of fractional calculus, nonextensive statistical mechanics, Tsallis statistics, superstatistics, the Mittag-Leffler stochastic process, the Lévi process and time series. Apart from examining the properties, the matrix-variate analogue and the connection to fractional calculus are also explained. By using the pathway model of Mathai, the model is further generalized. Connections to Mittag-Leffler distributions and corresponding autoregressive processes are also discussed.

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“…is given in Equation (51). But the structure in Equation (51) is that of a Mellin transform of a G-function of the type G p,0 p,p (·).…”

Section: Density Of the Volume Contentmentioning

confidence: 99%

“…Real-valued scalar functions of matrix argument, where the argument matrix is real and positive definite, are used in the extensions. In this regard, a matrix-variate pathway fractional integral operator is introduced, see [51] which may be regarded as a generalization of matrix-variate Riemann-Liouville fractional integral operator. Moreover, from this operator one can figure out all the matrix-variate fractional integrals and almost all the extended densities for the pathway parameter α < 1 and α → 1.…”

Section: Pathway Fractional Integralmentioning

confidence: 99%

An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences

Sebastian

Nair²,

Joseph³

2015

Axioms

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Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter α, called the pathway parameter, one can connect generalized type-1 beta family of densities, generalized type-2 beta family of densities, and generalized gamma family of densities, in the scalar as well as the matrix cases, also in the real and complex domains. It is shown that when the model is applied to physical situations then the current hot topics of Tsallis statistics and superstatistics in statistical mechanics become special cases of the pathway model, and the model is capable of capturing many stable situations as well as the unstable or chaotic neighborhoods of the stable situations and transitional stages. The pathway model is shown to be connected to generalized information measures or entropies, power law, likelihood ratio criterion or λ−criterion in multivariate statistical analysis, generalized Dirichlet densities, fractional calculus, Mittag-Leffler stochastic process, Krätzel integral in applied analysis, and many other topics in different disciplines. The pathway model enables one to extend the current results on quadratic and bilinear forms, when the samples come from Gaussian populations, to wider classes of populations.Axioms 2015, 4 531

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Pathway fractional integral operator and matrix-variate functions

Cited by 6 publications

References 10 publications

The pathway integral operator involving extension of k-Bessel-Maitland function

The pathway integral operator involving extension of k-Bessel-Maitland function

An Overview of Generalized Gamma Mittag–Leffler Model and Its Applications

An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences

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