Solution Of Fractional Kinetic Equation Research Articles

On the matrix versions of the k analog of ℑ‐incomplete Gauss hypergeometric functions and associated fractional calculus

In this paper, our aim is to introduce a new definition of ( ‐incomplete Wright hypergeometric matrix functions ( ‐IWHMFs) using the ‐incomplete Pochhammer matrix symbol. First, we define the ‐incomplete gamma matrix function and introduce the ‐incomplete Pochhammer matrix symbols. Furthermore, we present differential formulas and integral representation related to these ‐IWHMFs. We have also obtained some results regarding the ‐fractional calculus operators of these ‐IWHMFs. Finally, we investigate the solutions of fractional kinetic equations (FKEs) involving the ‐IWHMFs.

Analytic solutions of fractional kinetic equations involving incomplete ℵ-function

This paper expressed the fractional kinetic equation (KE) in terms of the incomplete [Formula: see text]-function, I-function, Fox H-function, and Meijer’s G-function. It assesses the importance of fractional KE in diverse scientific and engineering contexts, highlighting its relevance across various scenarios. In this paper, we investigate the results of Katugampola’s kinetic fractional equations with the product of the generalized M-series and incomplete [Formula: see text]-function. The [Formula: see text]-Laplace transform is applied for obtaining the desired results. Utilizing an M-series, the universality of this series is harnessed to deduce solutions for a fractional KE. Furthermore, a graphical representation of the obtained solutions’ behaviors is presented, enhancing the impact of the findings.

A new generalized beta function associated with statistical distribution and fractional kinetic equation

Several authors have extensively investigated beta function, hypergeometric function and confluent hypergeometric function, their extensions and generalizations due to their several application in many areas of engineering, probability theory and science. The main purpose of this paper is to present a new generalization of extended beta function, hypergeometric function and confluent hypergeometric function with the help of m-parameter Mittag-Leffler function, as well as examine some important properties like integral representations, differential formula and summation formulas. We also examine generalized Caputo fractional derivative operator with the help of m-parameter Mittag-Leffler function with associated properties using the generalized beta function. We define a new beta distribution involving the new generalized beta function. The mean, variance, coefficient of variance, moment generating function and characteristic function and cumulative distribution are derived. Further, we derive the solution of fractional Kinetic equation involving generalized hypergeometric function.

Solution of Fractional Kinetic Equations Involving Laguerre Polynomials via Sumudu Transform

This study focuses on calculating solutions for fractional kinetic equations involving Laguerre polynomials and their fractional derivatives. By leveraging the Sumudu transform technique, we derive these solutions in the form of the Mittag‐Leffler function. Our investigation includes graphical representations generated using MATLAB to illustrate the behavior of these solutions under varying parametric conditions. It is essential to note that the results obtained in this study are exceptionally versatile and have the potential to yield both established and potentially novel findings in this field of research.

On solution of fractional kinetic equation involving Riemann xi function via Sumudu transform

Several significant questions of mathematics and mathematical physics have been effectively explained and answered through the use of fractional kinetic equations containing special functions. Due to the high importance of arbitrary-order kinetic equations, the aim of this work is to obtain the solution of a new arbitrary-order kinetic equation related to the Riemann xi function. The Sumudu transform technique is used to solve it. The findings are plotted with the help of MATLAB R2016a. The outcomes of the paper are in the form of an infinite series representation of the Riemann xi function and in terms of the Mittag-Leffler function.

On some new inequalities and fractional kinetic equations associated with extended gauss hypergeometric and confluent hypergeometric function

Fractional kinetic equations are of immense importance in describing and solving numerous intriguing problems of physics and astrophysics. Inequalities are important topics in special functions. In this paper, we studied the monotonicity of the extended Gauss and confluent hypergeometric function that are derived by using the inequalities on generalized beta function involving Appell series and Lauricella function. We also establish generalized fractional kinetic equation involving extended hypergeometric and confluent hypergeometric functions. The solutions of generalized fractional kinetic equation is derived and studied as an application of extended hypergeometric and confluent hypergeometric function using the General integral transform. The results obtained here are general and can be used to derive many new solutions of fractional kinetic equations involving various types of special functions.

Solution of Fractional Kinetic Equations Involving generalized q−Bessel function

In this article, we pursue and examine the solutions to fractional kinetic equations that incorporate the q−Bessel function through their Sumudu transformations. An important special case is revealed in the process. The results obtained with the q− Bessel function are quite general in nature and can easily set up different new and known fractional kinetic equations.

Solution of fractional kinetic equation for Hadamard type fractional integral via Mellin transform

The aim of this paper is to introduce the generalized form of the fractional kinetic equation including Hadamard type fractional integral. We also present the solution of Kinetic equation including Hadamard type fractional integral with the help of generalized k-Wright function and Mellin transform. We also present the solution of Kinetic equation including Hadamard type fractional integral with the help of generalized Multindex Bessel Function and Mellin transform.

Solution of fractional kinetic equations involving extended $ (k, \tau) $-Gauss hypergeometric matrix functions

<abstract><p>In this work, we define an extension of the k-Wright ($ (k, \tau) $-Gauss) hypergeometric matrix function and obtain certain properties of this function. Further, we present this function to achieve the solution of the fractional kinetic equations.</p></abstract>

Solution of fractional kinetic equations involving generalized Hurwitz-Lerch Zeta function using Sumudu Transform

Fractional kinetic equations (FKEs) comprising a large array of special functions have been extensively and successfully applied in specification and solving many significant problems of astrophysics and physics. In this present work, our aim is to demonstrate solutions of (FKEs) of the generalized Hurwitz-Lerch Zeta function by applying the Sumudu transform. In addition to these, solutions of (FKEs) in special conditions of generalised Hurwitz-Lerch Zeta function have been derived.

On the Solution of Kinetic Equation for Katugampola Type Fractional Differential Equations

In this article, we have investigate a solution of fractional Kinetic equation involving Katugampola type fractional integral by using H – function. We also present the solution of Kinetic equation involving Katugampola type fractional integral with the help of generalized I – function and Mellin transform.

Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function

<p style='text-indent:20px;'>In this article, we have investigated certain definite integrals and various integral transforms of the generalized multi-index Bessel function, such as Euler transform, Laplace transform, Whittaker transform, K-transform and Fourier transforms. Also found the applications of the problem on fractional kinetic equation pertaining to the generalized multi-index Bessel function using the Sumudu transform technique. Mittage-Leffler function is used to express the results of the solutions of fractional kinetic equation as well as its special cases. The results obtained are significance in applied problems of science, engineering and technology.</p>

FRACTIONAL KINETIC EQUATIONS INVOLVING THE MITTAG-LEFFLER (p, s, k) FUNCTION VIA SUMUDU TRANSFORM

In this paper, we derive the solutions for fractional kinetic equations including the Mittag-Leffler function with the help of Laplace transform method. Further, the same fractional kinetic equation is solved by using the Sumudu transform. The results presented are in compact forms in the form of various type of Mittag-Leffler function etc. are also considered. We establish some corollary as special cases. Some new and known results are our findings.

Certain Image Formulae and Fractional Kinetic Equations of Generalized $$\mathtt {k}$$-Bessel Functions via the Sumudu Transform

The monotonicity and the representation formulae of generalized $$\mathtt {k}$$ -Bessel functions, $$W_{\nu ,c}^{\mathtt {k}}$$ , studied by SR Mondal. This paper establishes the image formulae and then extract the solutions for fractional kinetic equations, involving $$W_{\nu ,c}^{\mathtt {k}}$$ utilizing their Sumudu transforms. Some significant particular cases are then deduced and analyzed.

Fractional Calculus involving (p, q)-Mathieu Type Series

Abstract Aim of the present paper is to establish fractional integral formulas by using fractional calculus operators involving the generalized (p, q)-Mathieu type series. Then, their composition formulas by using the integral transforms are introduced. Further, a new generalized form of the fractional kinetic equation involving the series is also developed. The solutions of fractional kinetic equations are presented in terms of the Mittag-Leffler function. The results established here are quite general in nature and capable of yielding both known and new results.

Fractional Kinetic Equations Associated with Incomplete I-Functions

In this paper, we investigate the solution of fractional kinetic equation (FKE) associated with the incomplete I-function (IIF) by using the well-known integral transform (Laplace transform). The FKE plays a great role in solving astrophysical problems. The solutions are represented in terms of IIF. Next, we present some interesting corollaries by specializing the parameters of IIF in the form of simpler special functions and also mention a few known results, which are very useful in solving physical or real-life problems. Finally, some graphical results are presented to demonstrate the influence of the order of the fractional integral operator on the reaction rate.

Solution of fractional kinetic equations involving class of functions and Sumudu transform

Fractional kinetic equations (FKEs) including a wide variety of special functions have been widely and successfully applied in describing and solving many important problems of physics and astrophysics. In this paper, we derive the solutions for FKEs including the class of functions with the help of Sumudu transforms. Many important special cases are then revealed and analyzed. The use of the class of functions to obtain the solution of FKEs is fairly general and can be efficiently used to construct several well-known and novel FKEs.

Solutions of Fractional Kinetic Equation Associated with the Generalized Multiindex Bessel Function via Laplace Transform

This article is about finding the possible solutions of fractional kinetic equation associated with the generalized multiindex Bessel function using the method of Laplace transform. Numerical results and graphical solutions of the main theorems are also presented.

Solutions of fractional kinetic equation and the generalized Galué type Struve function

This paper aims to establish extensive form of the fractional kinetic equation involving generalized Galué type Struve function using the technique of Sumudu transform. Further, numerical values of the results are interpreted and their graphical interpretation of the solutions by employing MATLAB is given. The results obtained here are quite general and capable of yielding a very large number of known and new results.

Computable solution of fractional kinetic equations using Mathieu-type series

The Mathieu series appeared in the study of elasticity of solid bodies in the work of Émile Leonard Mathieu. Since then numerous authors have studied various problems arising from the Mathieu series in several diverse ways. In this line, our aim is to study the solution of fractional kinetic equations involving generalized Mathieu-type series. The generality of this series will help us to deduce results related to a fractional kinetic equation involving another form of Mathieu series. To obtain the solution, we use the Laplace transform technique. Besides, a graphical representation is given to observe the behavior of the obtained solutions.