Solution Of Fractional Kinetic Equation Research Articles

The generalized p-k-Mittag-Leffler function and solution of fractional kinetic equations

In this paper, we define the generalized p-k-Mittag-Leffler function and investigate its various important properties such as: Mellin-Barnes integral formula, integral transforms, and fractional calculus. The generalized p-k-Mittag-Leffler function is also discussed in terms of the solution of fractional kinetic equations. Certain interesting and useful examples are considered as special cases of generalized p-k-MLF to give the applications of our main results. We also point out their relevance with known results.

Solution of Fractional Kinetic Equations by Using Pα-Transform

The authors study a generalized form of fractional kinetic equations (FKE). The main results have been presented in the form of two theorems where in Pα-transform is used to obtain the solution of a generalized form of FKE containing τ -Gauss Hypergeometric functions and its derivatives. Some special cases of our main findings have also been recorded.

Fractional Kinetic Equation Involving Integral Transform

In this paper, we derive the solution of fractional kinetic equation with Laplace and Fourier transforms. Their respective solutions are given in terms of Mittag-Leffler function and their generalization, which can also be represented as Fox’s H-function. The result proved in this paper is application to wide range of engineering, astrophysics and physical science.

On fractional kinetic equations [formula omitted]-Struve functions based solutions

In the present research article, we investigate the solutions for fractional kinetic equations, involving k-Struve functions, some of the salient properties of which we present. The method used is Laplace transform based. The methodology and results can be adopted and extended to various related fractional problems in mathematical physics.

On the solutions of certain fractional kinetic equations involving k-Mittag-Leffler function

The aim of the present paper is to develop a new generalized form of the fractional kinetic equation involving a generalized k-Mittag-Leffler function E^{gamma,rho}_{k,zeta,eta}(cdot). The solutions of fractional kinetic equations are discussed in terms of the Mittag-Leffler function. Further, numerical values of the results and their graphical interpretation is interpreted to study the behavior of these solutions. The results established here are quite general in nature and capable of yielding both known and new results.

Closed-form solutions for the Lévy-stable distribution

The Lévy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas; for example, in economics it is used to model financial market fluctuations and in statistical mechanics it is used as a numerical solution of fractional kinetic equations of anomalous transport. This function does not have an explicit expression and no uniform solution has been proposed yet. This paper presents a uniform analytical approximation for the Lévy-stable distribution based on matching power series expansions. For this solution, the trans-stable function is defined as an auxiliary function which removes the numerical issues of the calculations of the Lévy-stable distribution. Then, the uniform solution is proposed as a result of an asymptotic matching between two types of approximations called "the inner solution" and "the outer solution." Finally, the results of analytical approximation are compared to the numerical results of the Lévy-stable distribution function, making this uniform solution valid to be applied as an analytical approximation.

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Dynamic k-Struve Sumudu solutions for fractional kinetic equations

In this present study, we investigate the solutions for fractional kinetic equations involving k-Struve function using the Sumudu transform. The graphical interpretations of the solutions involving k-Struve function and its comparison with generalized Bessel function are given. The methodology and results can be considered and applied to various related fractional problems in mathematical physics.

Fractional integrals and solution of fractional kinetic equations involving [formula omitted]-Mittag-Leffler function

In this paper, our main objective is to establish certain new fractional integral by applying the Saigo hypergeometric fractional integral operators and by employing some integral transforms on the resulting formulas, we presented their image formulas involving the product of the generalized k-Mittag-Leffler function. Furthermore, We develop a new and further generalized form of the fractional kinetic equation involving the product of the generalized k-Mittag-Leffler function. The manifold generality of the generalized k-Mittag-Leffler function is discussed in terms of the solution of the fractional kinetic equation and their graphical interpretation is interpreted in the present paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably) new results.

Solution of fractional kinetic equation by a class of integral transform of pathway type

Solutions of fractional kinetic equations are obtained through an integral transform named Pα-transform introduced in this paper. The Pα-transform is a binomial type transform containing many class of transforms including the well known Laplace transform. The paper is motivated by the idea of pathway model introduced by Mathai [Linear Algebra Appl. 396, 317–328 (2005)10.1016/j.laa.2004.09.022]. The composition of the transform with differential and integral operators are proved along with convolution theorem. As an illustration of applications to the general theory of differential equations, a simple differential equation is solved by the new transform. Being a new transform, the Pα-transform of some elementary functions as well as some generalized special functions such as H-function, G-function, Wright generalized hypergeometric function, generalized hypergeometric function, and Mittag-Leffler function are also obtained. The results for the classical Laplace transform is retrieved by letting α → 1.

Solutions of certain fractional kinetic equations and a fractional diffusion equation

In view of the usefulness and importance of kinetic equations in certain physical problems, the authors derive an explicit solution of a fractional kinetic equation of general character that unifies and extends earlier results. Further, an alternative shorter method based on a result developed by the authors is given to derive the solution of a fractional diffusion equation. Solutions are represented in terms of H-functions and generalized Mittag–Leffler functions.