Dark solitons and modulational instability of the nonlinear left-handed transmission electrical line with fractional derivative order

2020 ◽  
Vol 95 (10) ◽  
pp. 105803
Author(s):  
Djidere Ahmadou ◽  
Mibaile Justin ◽  
Boudoue M Hubert ◽  
Gambo Betchewe ◽  
Doka Yamigno Serge ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Modulational Instability ◽  
Dark Solitons ◽  
Left Handed ◽  
Derivative Order

scholarly journals Solitary waves and modulation instability with the influence of fractional derivative order in nonlinear left-handed transmission line

2021 ◽  
Author(s):  
Djidere Ahmadou ◽  
Alphonse Houwe ◽  
Justin Mibaile ◽  
Gambo Betchewe ◽  
Serge Y. Doka ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Transmission Line ◽  
Information And Communication Technologies ◽  
Solitary Waves ◽  
Fractional Derivatives ◽  
Modulation Instability ◽  
Gain Spectrum ◽  
Left Handed ◽  
Adomian Decomposition ◽  
Derivative Order

Abstract The resolution of the reduced fractional nonlinear Schrodinger equation obtained from the model describing the wave propagation in the left-handed nonlinear transmission line presented by Djidere et al recently, allowed us in this work through the Adomian decomposition method (ADM) to highlight the behavior and to study the propagation process of the dark and bright soliton solutions with the e ect of the fractional derivative order as well as the Modulation Instability gain spectrum (MI) in the LHNLTL. By inserting fractional derivatives in the sense of Caputo, we used ADM to structure the approximate solitons solutions of the fractional nonlinear Schrodinger equation reduced with fractional derivatives. The pipe is obtained from the bright and dark soliton by the fractional derivatives order (see Figures 2 and 5). By the bias of MI gain spectrum the instability zones occur when the value of the fractional derivative order tends to 1. Furthermore, when the fractional derivative order takes small values, stability zones appear. These results could bring new perspectives in the study of solitary waves in left-handed metamaterials, as the memory e ect could have a better future for the propagation of modulated waves because we also show in this article that the stabilization of zones of the dark and bright solitons could be described by a fractional nonlinear Schrodinger equation with small values of fractional derivatives order. In addition, the obtained signi cant results are new and could nd applications in many research areas such as in the eld of information and communication technologies.

scholarly journals Solitary waves and modulation instability with the influence of fractional derivative order in nonlinear left-handed transmission line

2021 ◽  
Vol 53 (7) ◽  
Author(s):  
Djidere Ahmadou ◽  
Houwe Alphonse ◽  
Mibaile Justin ◽  
Gambo Betchewe ◽  
Doka Yamigno Serge ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Transmission Line ◽  
Solitary Waves ◽  
Modulation Instability ◽  
Left Handed ◽  
Derivative Order

scholarly journals Analytical survey of the predator–prey model with fractional derivative order

AIP Advances ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 035127
Author(s):  
Souleymanou Abbagari ◽  
Alphonse Houwe ◽  
Youssoufa Saliou ◽  
\, Douvagaï ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Derivative Order

Half-lives of spherical proton emitters within the framework of fractional calculus

2014 ◽  
Vol 23 (09) ◽  
pp. 1450044 ◽  
Author(s):  
Abdullah Engin Çalik ◽  
Hüseyin Şirin ◽  
Hüseyin Ertik ◽  
Buket Öder ◽  
Mürsel Şen
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Nuclear Structure ◽  
Caputo Fractional Derivative ◽  
Half Life ◽  
Nuclear Decay ◽  
Life Values ◽  
Derivative Order

In this paper, the half-life values of spherical proton emitters such as Sb , Tm , Lu , Ta , Re , Ir , Au , Tl and Bi have been calculated within the framework of fractional calculus. Nuclear decay equation, related to this phenomenon, has been resolved by using Caputo fractional derivative. The order of fractional derivative μ being considered is 0 < μ ≤ 1, and characterizes the fractality of time. Half-life values have been calculated equivalent with empirical ones. The dependence of fractional derivative order μ on the nuclear structure has also been investigated.

scholarly journals The transversal creeping vibrations of a fractional derivative order constitutive relation of nonhomogeneous beam

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
Katica (Stevanovic) Hedrih
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Constitutive Relation ◽  
Continuous Functions ◽  
Beam Dynamic ◽  
Fractional Differential ◽  
Elastic Form ◽  
Partial Fractional Differential Equation ◽  
Derivative Order

We considered the problem on transversal oscillations of two-layer straight bar, which is under the action of the lengthwise random forces. It is assumed that the layers of the bar were made of nonhomogenous continuously creeping material and the corresponding modulus of elasticity and creeping fractional order derivative of constitutive relation of each layer are continuous functions of the length coordinate and thickness coordinates. Partial fractional differential equation and particular solutions for the case of natural vibrations of the beam of creeping material of a fractional derivative order constitutive relation in the case of the influence of rotation inertia are derived. For the case of natural creeping vibrations, eigenfunction and time function, for different examples of boundary conditions, are determined. By using the derived partial fractional differential equation of the beam vibrations, the almost sure stochastic stability of the beam dynamic shapes, corresponding to thenth shape of the beam elastic form, forced by a bounded axially noise excitation, is investigated. By the use of S. T. Ariaratnam's idea, as well as of the averaging method, the top Lyapunov exponent is evaluated asymptotically when the intensity of excitation process is small.

Interaction of two dark solitons in nonlinear left-handed materials

Optik ◽  
2012 ◽  
Vol 123 (18) ◽  
pp. 1597-1600 ◽  
Author(s):  
Dongqi Yang ◽  
Jieqiu Zhang ◽  
Jianqi Zhang ◽  
Xiaorui Wang ◽  
Jiafu Wang ◽  
...  
Keyword(s):  
Dark Solitons ◽  
Left Handed

Free Vibration of Elastic Timoshenko Beam on Fractional Derivative Winkler Viscoelastic Foundation

2011 ◽  
Vol 368-373 ◽  
pp. 1034-1037 ◽  
Author(s):  
Qi Fang Yan ◽  
Zi Ping Su
Keyword(s):  
Free Vibration ◽  
Fractional Derivative ◽  
Shear Deformation ◽  
Timoshenko Beam ◽  
Shape Factor ◽  
Viscoelastic Foundation ◽  
Deformation Function ◽  
Numerical Example ◽  
Foundation Model ◽  
Derivative Order

The fractional derivative Winkler viscoelastic foundation model is established by introducing the concept of fractional derivative. The control equations of free vibration of elastic Timoshenko beam on fractional derivative Winkler viscoelastic foundation are also built by considering the shear deformation and rotary inertia, and the control equations of elastic Timoshenko beam are decoupled by using the deformation function and considering the properties of fractional derivative, and the expressions of deflection and section corner of elastic Timoshenko beam on fractional derivative Winkler viscoelastic foundation are obtained. The influences of fractional derivative order and shear shape factor on the free vibration of elastic Timoshenko beam are discussed by numerical example.

Numerical and analytical solutions of nonlinear differential equations involving fractional operators with power and Mittag-Leffler kernel

2018 ◽  
Vol 13 (1) ◽  
pp. 13 ◽  
Author(s):  
H. Yépez-Martínez ◽  
J.F. Gómez-Aguilar
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Nonlinear Differential Equations ◽  
Fractional Operators ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractional Differential ◽  
Derivative Order

Analytical and numerical simulations of nonlinear fractional differential equations are obtained with the application of the homotopy perturbation transform method and the fractional Adams-Bashforth-Moulton method. Fractional derivatives with non singular Mittag-Leffler function in Liouville-Caputo sense and the fractional derivative of Liouville-Caputo type are considered. Some examples have been presented in order to compare the results obtained, classical behaviors are recovered when the derivative order is 1.

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