Integral Transform and the Solution of Fractional Kinetic Equation Involving Some Special Functions

2018 ◽  
Vol 55 (2) ◽  
pp. 127-136
Author(s):  
S.K.Shar ma ◽  
A.S.Shek hawat
Keyword(s):  
Kinetic Equation ◽  
Integral Transform ◽  
Special Functions ◽  
Fractional Kinetic Equation

scholarly journals Fractional Kinetic Equations Associated with Incomplete I-Functions

2020 ◽  
Vol 4 (2) ◽  
pp. 19 ◽  
Author(s):  
Manish Kumar Bansal ◽  
Devendra Kumar ◽  
Priyanka Harjule ◽  
Jagdev Singh
Keyword(s):  
Fractional Integral ◽  
Reaction Rate ◽  
Integral Transform ◽  
Special Functions ◽  
Kinetic Equations ◽  
Real Life ◽  
Great Role ◽  
Fractional Kinetic Equation ◽  
Life Problems ◽  
Fractional Kinetic Equations

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.

scholarly journals Solution of generalized fractional kinetic equation in terms of special functions

2014 ◽  
Vol 9 ◽  
pp. 1647-1657
Author(s):  
Ahmad Faraj ◽  
Tariq Salim ◽  
Safaa Sadek ◽  
Jamal Ismail
Keyword(s):  
Kinetic Equation ◽  
Special Functions ◽  
Fractional Kinetic Equation

FRACTIONAL KINETIC EQUATIONS INVOLVING GENERALIZED V-FUNCTION VIA LAPLACE TRANSFORM

2021 ◽  
Vol 10 (5) ◽  
pp. 2593-2610
Author(s):  
Wagdi F.S. Ahmed ◽  
D.D. Pawar ◽  
W.D. Patil
Keyword(s):  
Kinetic Equation ◽  
Laplace Transform ◽  
Kinetic Equations ◽  
Graphical Interpretation ◽  
Fractional Kinetic Equation ◽  
Fractional Kinetic Equations

In this study, a new and further generalized form of the fractional kinetic equation involving the generalized V$-$function has been developed. We have discussed the manifold generality of the generalized V$-$function in terms of the solution of the fractional kinetic equation. Also, the graphical interpretation of the solutions by employing MATLAB is given. The results are very general in nature, and they can be used to generate a large number of known and novel results.

scholarly journals Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Special Functions ◽  
Integral Transforms ◽  
Integral Formulas ◽  
Special Cases

A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving theFp(α,β)(·). In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functionsFp(α,β,m)(·). Some interesting special cases of our main results are also considered.

scholarly journals Fractional kinetic equations driven by Gaussian or infinitely divisible noise

2005 ◽  
Vol 37 (2) ◽  
pp. 366-392 ◽  
Author(s):  
J. M. Angulo ◽  
V. V. Anh ◽  
R. McVinish ◽  
M. D. Ruiz-Medina
Keyword(s):  
Kinetic Equation ◽  
Kinetic Equations ◽  
Unbounded Domains ◽  
Long Range Dependence ◽  
Infinitely Divisible ◽  
Fractional Kinetic Equation ◽  
Noise Input ◽  
Spatial Operators ◽  
Fractional Kinetic Equations

In this paper, we consider a certain type of space- and time-fractional kinetic equation with Gaussian or infinitely divisible noise input. The solutions to the equation are provided in the cases of both bounded and unbounded domains, in conjunction with bounds for the variances of the increments. The role of each of the parameters in the equation is investigated with respect to second- and higher-order properties. In particular, it is shown that long-range dependence may arise in the temporal solution under certain conditions on the spatial operators.

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

2020 ◽  
Vol 5 (2) ◽  
pp. 15-34 ◽  
Author(s):  
Daljeet Kaur ◽  
Praveen Agarwal ◽  
Madhuchanda Rakshit ◽  
Mehar Chand
Keyword(s):  
Kinetic Equation ◽  
Fractional Calculus ◽  
Fractional Integral ◽  
Kinetic Equations ◽  
Integral Transforms ◽  
Type Series ◽  
Integral Formulas ◽  
Fractional Kinetic Equation ◽  
Fractional Calculus Operators ◽  
Fractional Kinetic Equations

AbstractAim 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.

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

2019 ◽  
Vol 22 (7) ◽  
pp. 1167-1184 ◽  
Author(s):  
D. L. Suthar ◽  
Haile Habenom ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Kinetic Equation ◽  
Fractional Kinetic Equation
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