EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

Multivariable Function과 그의 合成에 있어서의 問題點

In this paper, we introduce a Laplace-type integral transform called the Shehu transform which is a generalization of the Laplace and the Sumudu integral transforms for solving differential equations in the time domain. The proposed integral transform is successfully derived from the classical Fourier integral transform and is applied to both ordinary and partial differential equations to show its simplicity, efficiency, and the high accuracy.

New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations

A nonlinear quantum boundary value problem (q-FBVP) formulated in the sense of quantum Caputo derivative, with fractional q-integro-difference conditions along with its fractional quantum-difference inclusion q-BVP are investigated in this research. To prove the solutions’ existence for these quantum systems, we rely on the notions such as the condensing functions and approximate endpoint criterion (AEPC). Two numerical examples are provided to apply and validate our main results in this research work.

Condensing Functions and Approximate Endpoint Criterion for the Existence Analysis of Quantum Integro-Difference FBVPs

New integral transform: Shehu transform a generalization of Sumudu and Laplace transform for solving differential equations

The present paper introduces q-analogues of the Sumudu transform and derives some distinct properties, for example its convergence conditions and certain interesting connection theorems involving q-Laplace transforms. Furthermore, certain fundamental properties of q-Sumudu transforms like, linearity, shifting theorems, differentiation and integration etc. have also been investigated. An attempt has also been made to obtain the convolution theorem for the q-Sumudu transform of a function which can be expressed as a convergent infinite series.

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On q-Analogues of Sumudu Transform

Although Sumudu transform is the theoritical dual of the Laplace transform, it has many applications in sciences and engineering for its special fundamental properties. In a previous paper (3), we studied q-analogues of the Sumudu transform and derived some fundamental properties. This paper follows the previous paper and aims to provide some applications of the q-Sumudu transform. The authors give q-Sumudu transforms of some q-polynomials and q-functions. Also, we evaluated the q-Sumudu transform of basic analogue of Fox's H-function.

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On q-Sumudu Transforms of Certain q-Polynomials

In this work, two q-Laplace type integral transforms called -transform and -transform are introduced. Some properties of q-analogues of the -transform are given, and several relationships between them are studied. Moreover, we show that the new Laplace type q-integral transforms may be regarded as q-extension of the ℒ2-transform. Some illustrative examples are also given.

On q-Laplace type integral operators and their applications

The main purpose of this paper is to evaluate -Sumudu transforms of a product of -Bessel functions. Interesting special cases of theorems are also discussed. Further, the results proved in this paper may find certain applications of -Sumudu transforms to the solutions of the -integrodifferential equations involving -Bessel functions. The results may help to extend the -theory of orthogonal functions.

https://downloads.hindawi.com/journals/tswj/2014/327019.pdf

-Sumudu Transforms of -Analogues of Bessel Functions

The aim of this paper is to give an alternative solution for the $q$-kinetic equation involving the Riemann--Liouville fractional $q$-integral operator. The solution is obtained in terms of the $q$-Mittag--Leffler functions using inverse $q$-Sumudu transform. As applications, some corollaries are presented to illustrate the main results.

/pdf/an-application-of-q-sumudu-transform-for-fractional-q-46g8zayxc2.pdf

Faruk Uçar

Papers

On q-Analogues of Sumudu Transform

On q-Sumudu Transforms of Certain q-Polynomials

On q-Laplace type integral operators and their applications

-Sumudu Transforms of -Analogues of Bessel Functions

An application of q-Sumudu transform for fractional q-kinetic equation