FRACTIONAL KINETIC EQUATIONS INVOLVING GENERALIZED V-FUNCTION VIA LAPLACE TRANSFORM

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.

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

Applied Mathematics and Nonlinear Sciences ◽

10.2478/amns.2020.2.00011 ◽

2020 ◽

Vol 5 (2) ◽

pp. 15-34 ◽

Cited By ~ 4

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.

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Fractional kinetic equations driven by Gaussian or infinitely divisible noise

Advances in Applied Probability ◽

10.1017/s0001867800000227 ◽

2005 ◽

Vol 37 (02) ◽

pp. 366-392 ◽

Cited By ~ 5

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.

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Application of Laplace Transform on Fractional Kinetic Equation Pertaining to the Generalized Galué Type Struve Function

Advances in Mathematical Physics ◽

10.1155/2019/5074039 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Haile Habenom ◽

D. L. Suthar ◽

Melaku Gebeyehu

Keyword(s):

Kinetic Equation ◽

Laplace Transform ◽

Laplace Transforms ◽

Extensive Form ◽

Graphical Interpretation ◽

Fractional Kinetic Equation

In this paper, we establish extensive form of the fractional kinetic equation involving generalized Galué type Struve function using the technique of Laplace transforms. The results are expressed in terms of Mittag-Leffler function. Further, numerical values of the results and their graphical interpretation are interpreted to study the behaviour of these solutions. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably) new results.

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On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind

Mathematical Problems in Engineering ◽

10.1155/2015/289387 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7 ◽

Cited By ~ 17

Author(s):

Dinesh Kumar ◽

S. D. Purohit ◽

A. Secer ◽

A. Atangana

Keyword(s):

Kinetic Equation ◽

Bessel Function ◽

Kinetic Equations ◽

Generalized Bessel Function ◽

Fractional Kinetic Equation ◽

Fractional Kinetic Equations

We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably) new results.

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Solution of Fractional Kinetic Equations Associated with the p,q-Mathieu-Type Series

Discrete Dynamics in Nature and Society ◽

10.1155/2020/8645161 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

D. L. Suthar ◽

S. D. Purohit ◽

Serkan Araci

Keyword(s):

Kinetic Equation ◽

Kinetic Equations ◽

Laplace Transforms ◽

Type Series ◽

Fractional Kinetic Equation ◽

Fractional Kinetic Equations

In this paper, our aim is to finding the solutions of the fractional kinetic equation related with the p,q-Mathieu-type series through the procedure of Sumudu and Laplace transforms. The outcomes of fractional kinetic equations in terms of the Mittag-Leffler function are presented.

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Further Developments of Bessel Functions via Conformable Calculus with Applications

Journal of Function Spaces ◽

10.1155/2021/6069201 ◽

2021 ◽

Vol 2021 ◽

pp. 1-17

Author(s):

Mahmoud Abul-Ez ◽

Mohra Zayed ◽

Ali Youssef

Keyword(s):

Differential Equations ◽

Fractional Calculus ◽

Laplace Transform ◽

Bessel Functions ◽

Kinetic Equations ◽

Test Problems ◽

Physical Problems ◽

Starting Point ◽

Fractional Differential ◽

Fractional Kinetic Equations

The theory of Bessel functions is a rich subject due to its essential role in providing solutions for differential equations associated with many applications. As fractional calculus has become an efficient and successful tool for analyzing various mathematical and physical problems, the so-called fractional Bessel functions were introduced and studied from different viewpoints. This paper is primarily devoted to the study of developing two aspects. The starting point is to present a fractional Laplace transform via conformable fractional-order Bessel functions (CFBFs). We establish several important formulas of the fractional Laplace Integral operator acting on the CFBFs of the first kind. With this in hand, we discuss the solutions of a generalized class of fractional kinetic equations associated with the CFBFs in view of our proposed fractional Laplace transform. Next, we derive an orthogonality relation of the CFBFs, which enables us to study an expansion of any analytic functions by means of CFBFs and to propose truncated CFBFs. A new approximate formula of conformable fractional derivative based on CFBFs is provided. Furthermore, we describe a useful scheme involving the collocation method to solve some conformable fractional linear (nonlinear) multiorder differential equations. Accordingly, several practical test problems are treated to illustrate the validity and utility of the proposed techniques and examine their approximate and exact solutions. The obtained solutions of some fractional differential equations improve the analog ones provided by various authors using different techniques. The provided algorithm may be beneficial to enrich the Bessel function theory via fractional calculus.

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Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction

Abstract and Applied Analysis ◽

10.1155/2013/610314 ◽

2013 ◽

Vol 2013 ◽

pp. 1-19 ◽

Cited By ~ 19

Author(s):

Ferial Ghaemi ◽

Robiah Yunus ◽

Ali Ahmadian ◽

Soheil Salahshour ◽

Mohamed Suleiman ◽

...

Keyword(s):

Kinetic Equation ◽

Legendre Polynomials ◽

Chemical Engineering ◽

Kinetic Equations ◽

Hydrolysis Reaction ◽

Specific Chemical ◽

Fractional Differential ◽

Fractional Kinetic Equations ◽

Fractional Equation ◽

Fuzzy Fractional Differential Equations

In view of the usefulness and a great importance of the kinetic equation in specific chemical engineering problems, we discuss the numerical solution of a simple fuzzy fractional kinetic equation applied for the hemicelluloses hydrolysis reaction. The fuzzy approximate solution is derived based on the Legendre polynomials to the fuzzy fractional equation calculus. Moreover, the complete error analysis is explained based on the application of fuzzy Caputo fractional derivative. The main advantage of the present method is its superior accuracy which is obtained by using a limited number of Legendre polynomials. The method is computationally interesting, and the numerical results demonstrate the effectiveness and validity of the method for solving fuzzy fractional differential equations.

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On a class of stochastic fractional kinetic equation with fractional noise

Advances in Difference Equations ◽

10.1186/s13662-021-03284-1 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Min Lu ◽

Junfeng Liu

Keyword(s):

Kinetic Equations ◽

Upper Bounds ◽

Lower And Upper Bounds ◽

Riesz Potentials ◽

Diffusion Operator ◽

Fractional Noise ◽

Mild Conditions ◽

Fractional Kinetic Equation ◽

Time Variables ◽

Fractional Kinetic Equations

AbstractIn this article we study a class of stochastic fractional kinetic equations with fractional noise which are spatially homogeneous and are fractional in time with $H>1/2$ H > 1 / 2 . The diffusion operator involved in the equation is the composition of the Bessel and Riesz potentials with any fractional parameters. We prove the existence of the solution under some mild conditions which generalized some results obtained by Dalang (Electron. J. Probab. 4(6):1–29, 1999) and Balan and Tudor (Stoch. Process. Appl. 120:2468–2494 , 2010). We study also its Hölder continuity with respect to space and time variables with $b=0$ b = 0 . Moreover, we prove the existence for the density of the solution and establish the Gaussian-type lower and upper bounds for the density by the techniques of Malliavin calculus.

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LIOUVILLE AND BOGOLIUBOV EQUATIONS WITH FRACTIONAL DERIVATIVES

Modern Physics Letters B ◽

10.1142/s0217984907012700 ◽

2007 ◽

Vol 21 (05) ◽

pp. 237-248 ◽

Cited By ~ 14

Author(s):

VASILY E. TARASOV

Keyword(s):

Liouville Equation ◽

Fractional Derivatives ◽

Kinetic Equations ◽

Charged Particles ◽

Volume Element ◽

Vlasov Equations ◽

Fractional Kinetic Equation ◽

Derivatives Of ◽

Bogoliubov Equations ◽

Fractional Kinetic Equations

The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generalization of the Hamiltonian systems is discussed. Fractional kinetic equation for the system of charged particles are considered.

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