. A remarkably large number of integral formulas involving avariety of special functions have been developed by many authors. Alsomany integral formulas involving various Bessel functions have been pre-sented. Very recently, Choi and Agarwal derived two generalized integralformulas associated with the Bessel function J ν (z) of the ﬁrst kind, whichare expressed in terms of the generalized (Wright) hypergeometric func-tions. In the present sequel to Choi and Agarwal’s work, here, in thispaper, we establish two new integral formulas involving the generalizedBessel functions, which are also expressed in terms of the generalized(Wright) hypergeometric functions. Some interesting special cases of ourtwo main results are presented. We also point out that the results pre-sented here, being of general character, are easily reducible to yield manydiverse new and known integral formulas involving simpler functions. 1. Introduction and preliminariesA remarkably large number of integral formulas involving a variety of spe-cial functions have been developed by many authors (see, e.g., [5], [7] and [9];for a very recent work, see also [6]). Many integral formulas involving prod-ucts of Bessel functions have been developed and play an important role inseveral physical problems. In fact, Bessel functions are associated with a widerange of problems in diverse areas of mathematical physics, for example, thosein acoustics, radio physics, hydrodynamics, and atomic and nuclear physics.These connections of Bessel functions with various other research areas haveled many researchers to the ﬁeld of special functions. Among many propertiesof Bessel functions, they also have investigated some possible extensions of theBessel functions. A useful generalization w

/pdf/certain-new-integral-formulas-involving-the-generalized-1n5z1kvcfs.pdf

Certain new integral formulas involving the generalized bessel functions

We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably) new results.

/pdf/on-generalized-fractional-kinetic-equations-involving-44mchlsnrv.pdf

On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind

Two integral operators involving Appell's functions, or Horn's function in the kernel are considered. Composition of such functions with generalized Bessel functions of the first kind is expressed in terms of generalized Wright function and generalized hypergeometric series. Many special cases, including cosine and sine function, are also discussed.

/pdf/marichev-saigo-maeda-fractional-integration-operators-2854cjmeoo.pdf

Marichev-Saigo-Maeda Fractional Integration Operators Involving Generalized Bessel Functions

Complex diseases progression can be generally divided into three states, which are normal state, predisease/critical state and disease state. The sudden deterioration of diseases can be viewed as a bifurcation or a critical transition. Therefore, hunting for the tipping point or critical state is of great importance to prevent the disease deterioration. However, it is still a challenging task to detect the critical states of complex diseases with high-dimensional data, especially based on an individual. In this study, we develop a new method based on network fluctuation of molecules, temporal network flow entropy (TNFE) or temporal differential network flow entropy, to detect the critical states of complex diseases on the basis of each individual. By applying this method to a simulated dataset and six real diseases, including respiratory viral infections and tumors with four time-course and two stage-course high-dimensional omics datasets, the critical states before deterioration were detected and their dynamic network biomarkers were identified successfully. The results on the simulated dataset indicate that the TNFE method is robust under different noise strengths, and is also superior to the existing methods on detecting the critical states. Moreover, the analysis on the real datasets demonstrated the effectiveness of TNFE for providing early-warning signals on various diseases. In addition, we also predicted disease deterioration risk and identified drug targets for cancers based on stage-wise data. 

OUP accepted manuscript

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, r...

Bifurcation and chaos in a discrete predator–prey model with holling type-iii functional response and harvesting effect

Generalizing the classical Riemann-Liouville and Erdeyi-Kober fractional integral operators two integral transforms involving Gaussian hypergeometric functions in the kernel are considered. Formulas for composition of such integrals with generalized Bessel function of the first kind are obtained. Special cases involving trigonometric functions such as sine, cosine, hyperbolic sine and hyperbolic cosine are deduced. These results are established in terms of generalized Wright function and generalized hypergeometric functions.Copyright © 2011 by ASME

Fractional integration of generalized bessel function of the first kind

Derivatives of a finite class of orthogonal polynomials related to inverse Gamma distribution

Among the six classes of classical orthogonal polynomials, three of them are infinite, namely Jacobi, Hermite and Laguerre and the remaining three are finite and characterized by Masjed Jamei (2002) [5]. In this work, we consider derivatives of one such finite class of orthogonal polynomials that are orthogonal with respect to the weight function which is related to the probability density function of the F distribution. For this derivative class, besides orthogonality we find various other related properties such as the normal form and the self adjoint form. The corresponding Gaussian quadrature formulae are also given. Examples are provided to support the advantages of considering this derivative class of the finite class of orthogonal polynomials.

Derivatives of a finite class of orthogonal polynomials defined on the positive real line related to F-distribution

In this work, a Leslie–Gower prey-predator model with two discrete delays has been investigated. The positivity, boundedness and persistence of the delayed system have been discussed. The system ex...

Hopf bifurcation and chaos in a Leslie–Gower prey–predator model with discrete delays

Some composition formulas of jacobi type orthogonal polynomials

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