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

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
Moheb Saad Abouzaid ◽  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Bessel Functions ◽  
Kinetic Equations ◽  
Sumudu Transform ◽  
Fractional Kinetic Equations

scholarly journals Further Developments of Bessel Functions via Conformable Calculus with Applications

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.

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

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Kottakkaran Sooppy Nisar ◽  
Amjad Shaikh ◽  
Gauhar Rahman ◽  
Dinesh Kumar
Keyword(s):  
Kinetic Equations ◽  
Sumudu Transform ◽  
Class Of Functions ◽  
Fractional Kinetic Equations

scholarly journals Fractional kinetic equations involving generalized k-Bessel function via Sumudu transform

2018 ◽  
Vol 57 (3) ◽  
pp. 1937-1942 ◽  
Author(s):  
P. Agarwal ◽  
S.K. Ntouyas ◽  
S. Jain ◽  
M. Chand ◽  
G. Singh
Keyword(s):  
Bessel Function ◽  
Kinetic Equations ◽  
Sumudu Transform ◽  
Fractional Kinetic Equations

Application of q-Bessel Functions in the Solution of Generalized Fractional Kinetic Equations

2021 ◽  
Vol 88 (1-2) ◽  
pp. 01
Author(s):  
Garima Agarwal ◽  
Sunil Joshi ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Laplace Transform ◽  
Bessel Function ◽  
Bessel Functions ◽  
Kinetic Equations ◽  
Mathematical Physics ◽  
The Laplace Transform ◽  
Fractional Kinetic Equations

The present investigation aims to extract a solution from the generalized fractional kinetic equations involving the generalized q-Bessel function by applying the Laplace transform. Methodology and results can be adopted and extended to a variety of related fractional problems in mathematical physics.

AN APPROACH OF SUMUDU TRANSFORM TO FRACTIONAL KINETIC EQUATIONS

2020 ◽  
Vol 9 (9) ◽  
pp. 7045-7056
Author(s):  
Komal Prasad Sharma ◽  
Alok Bhargava
Keyword(s):  
Kinetic Equations ◽  
Sumudu Transform ◽  
Fractional Kinetic Equations

scholarly journals On Image Formulae Leading to Fractional Kinetic Equations Solutions via Sumudu Generalized k-Bessel Functions

2017 ◽  
Author(s):  
Kottakkaran S. Nisar ◽  
Moheb S. Abouzaid ◽  
Fethi Bin M. Belgacem
Keyword(s):  
Bessel Functions ◽  
Kinetic Equations ◽  
Monotonicity Properties ◽  
Special Cases ◽  
Fractional Kinetic Equations ◽  
Sumudu Transforms

Recently, representation formulae and monotonicity properties of generalized k-Bessel functions, Wk v,c., were established and studied by SR Mondal [24]. In this paper, we pursue and investigate some of their image formulae. We then extract solutions for fractional kinetic equations, involving Wk v,c, by means of their Sumudu transforms. In the process, Important special cases are then revealed, and analyzed.

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.

The “Fractional” Kinetic Equations and General Theory of Dielectric Relaxation

2005 ◽  
Author(s):  
Raoul R. Nigmatullin
Keyword(s):  
General Theory ◽  
Dielectric Relaxation ◽  
Collective Motion ◽  
Kinetic Equations ◽  
Heterogeneous Materials ◽  
Complex Conjugate ◽  
Electric Circuits ◽  
Self Similar ◽  
Fractional Kinetic Equations ◽  
Frequency Temperature

Based on the Mori-Zwanzig formalism it becomes possible to suggest a general decoupling procedure, which reduces a wide set of various micromotions distributed over a self-similar structure to a few collective/reduced motions describing the relaxation/exchange behavior of a complex system in the mesoscale region. The frequency dependence of the reduced collective motion contains real and pair of complex-conjugate power-law exponents in the frequency domain and explains naturally the “universal response” (UR) phenomenon discovered by A. Jonscher in a wide class of heterogeneous materials. This strict mathematical result allows in developing a consistent and general theory of dielectric relaxation that can describe wide set of dielectric spectroscopy (DS) data measured in some frequency/temperature range in many heterogeneous materials. Based on this result it becomes possible also to suggest a new set of two-pole elements, which generalizes the conventional RLC-elements and can constitute the basis of new theory of the linear electric circuits.

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