Talha Usman - Academia.edu (original) (raw)

Papers by Talha Usman

Symmetry

In this article, we obtain certain finite integrals concerning generalized Mittag–Leffler functio... more In this article, we obtain certain finite integrals concerning generalized Mittag–Leffler functions, which are evaluated in terms of the generalized Fox–Wright function. The integrals of concern are unified in nature and thereby yield some new integral formulas as special cases. Moreover, we numerically compute some integrals using the Gaussian quadrature formula and draw a comparison with the main integrals by using graphical numerical investigation.

Honam Mathematical Journal, Mar 1, 2019

In the last decades, various integral formulas associated with Bessel functions of different kind... more In the last decades, various integral formulas associated with Bessel functions of different kinds as well as Bessel functions themselves, have been studied and a noteworthy amount of work can be found in the literature. Following up, we present two definite integral formulas involving the product of generalized Bessel function associated with orthogonal polynomials. Also, some intriguing special cases of our main results have been discussed.

Infosys Science Foundation Series, 2021

Since the World Health Organization has declared Coronavirus a pandemic, researchers have given s... more Since the World Health Organization has declared Coronavirus a pandemic, researchers have given several interpretations on how this virus is spreads. In the present work, in anticipation of substantial fatal effects on health of people following this human-to-human spread, we aim to propose a new six parameter-modified Weibull distribution to analyze the spread of Covid-19 virus. We apply this model to study the cumulative cases infected in some countries, we give a global analysis of the statistical data of the pandemic, and we prove that our new distribution efficiently generalizes some existing models and fits correctly some data registered from February to June 2020. We use these results to assess the potential for human-to-human spread to occur around the globe.

Kragujevac Journal of Mathematics, 2020

The special polynomials of more than one variable provide new means of analysis for the solutions... more The special polynomials of more than one variable provide new means of analysis for the solutions of a wide class of partial differential equations often encountered in physical problems. Motivated by their importance and potential for applications in a variety of research fields, recently, numerous polynomials and their extensions have been introduced and investigated. In this paper, we introduce a new family of Laguerre-based generalized Hermite-Euler polynomials, which are related to the Hermite, Laguerre and Euler polynomials and numbers. The results presented in this paper are based upon the theory of the generating functions. We derive summation formulas and related bilateral series associated with the newly introduced generating function. We also point out that the results presented here, being very general, can be specialized to give many known and new identities and formulas involving relatively simple numbers and polynomials.

New Trends in Mathematical Science, 2016

In recent years, integral formulas involving a variety of special functions have been developed b... more In recent years, integral formulas involving a variety of special functions have been developed by a number of authors. Recently Khan and Ghayasuddin established some interesting unified integrals involving Whittaker function, generalized Bessel function and generalized Bessel-Maitland functions. In the present paper, we aim at establishing two new generalized integral formulas involving Whittaker function of first kind M k,µ (z), which are expressed in terms of Kampé de Fériet functions. Our integrals are unified in nature and act as key formulas from which we also derived some special cases.

Inspired by the framework of operational methods and based on the generating functions of Legendr... more Inspired by the framework of operational methods and based on the generating functions of Legendre-Gould Hopper polynomials and Sheffer sequences, we discuss certain new mixed type polynomials and their important properties. We show that the use of operational nature allows the relevant polynomials to be unified and general in nature. It is illustrated how the polynomials, we develop, provide an easy derivation of a wide class of new and known polynomials, and their respective properties.

Symmetry

In this article, we obtain certain finite integrals concerning generalized Mittag–Leffler functio... more In this article, we obtain certain finite integrals concerning generalized Mittag–Leffler functions, which are evaluated in terms of the generalized Fox–Wright function. The integrals of concern are unified in nature and thereby yield some new integral formulas as special cases. Moreover, we numerically compute some integrals using the Gaussian quadrature formula and draw a comparison with the main integrals by using graphical numerical investigation.

Honam Mathematical Journal, Mar 1, 2019

In the last decades, various integral formulas associated with Bessel functions of different kind... more In the last decades, various integral formulas associated with Bessel functions of different kinds as well as Bessel functions themselves, have been studied and a noteworthy amount of work can be found in the literature. Following up, we present two definite integral formulas involving the product of generalized Bessel function associated with orthogonal polynomials. Also, some intriguing special cases of our main results have been discussed.

Infosys Science Foundation Series, 2021

Since the World Health Organization has declared Coronavirus a pandemic, researchers have given s... more Since the World Health Organization has declared Coronavirus a pandemic, researchers have given several interpretations on how this virus is spreads. In the present work, in anticipation of substantial fatal effects on health of people following this human-to-human spread, we aim to propose a new six parameter-modified Weibull distribution to analyze the spread of Covid-19 virus. We apply this model to study the cumulative cases infected in some countries, we give a global analysis of the statistical data of the pandemic, and we prove that our new distribution efficiently generalizes some existing models and fits correctly some data registered from February to June 2020. We use these results to assess the potential for human-to-human spread to occur around the globe.

Kragujevac Journal of Mathematics, 2020

The special polynomials of more than one variable provide new means of analysis for the solutions... more The special polynomials of more than one variable provide new means of analysis for the solutions of a wide class of partial differential equations often encountered in physical problems. Motivated by their importance and potential for applications in a variety of research fields, recently, numerous polynomials and their extensions have been introduced and investigated. In this paper, we introduce a new family of Laguerre-based generalized Hermite-Euler polynomials, which are related to the Hermite, Laguerre and Euler polynomials and numbers. The results presented in this paper are based upon the theory of the generating functions. We derive summation formulas and related bilateral series associated with the newly introduced generating function. We also point out that the results presented here, being very general, can be specialized to give many known and new identities and formulas involving relatively simple numbers and polynomials.

New Trends in Mathematical Science, 2016

In recent years, integral formulas involving a variety of special functions have been developed b... more In recent years, integral formulas involving a variety of special functions have been developed by a number of authors. Recently Khan and Ghayasuddin established some interesting unified integrals involving Whittaker function, generalized Bessel function and generalized Bessel-Maitland functions. In the present paper, we aim at establishing two new generalized integral formulas involving Whittaker function of first kind M k,µ (z), which are expressed in terms of Kampé de Fériet functions. Our integrals are unified in nature and act as key formulas from which we also derived some special cases.

Inspired by the framework of operational methods and based on the generating functions of Legendr... more Inspired by the framework of operational methods and based on the generating functions of Legendre-Gould Hopper polynomials and Sheffer sequences, we discuss certain new mixed type polynomials and their important properties. We show that the use of operational nature allows the relevant polynomials to be unified and general in nature. It is illustrated how the polynomials, we develop, provide an easy derivation of a wide class of new and known polynomials, and their respective properties.