Wyniki wyszukiwania - BazTech

1

Novel soliton solutions for the fractional three-wave resonant interaction equations

Alqaraleh Sahar M., Talafha Adeeb G.

Demonstratio Mathematica

|

2022

|

Vol. 55, nr 1

490--505

EN

In this article, we obtained new infinite sets of exact soliton solutions for the nonlinear evolution system of three-wave resonant interaction equations. The solved system contains the non-zero second-order dispersion coefficients, the non-zero phase velocity mismatch, and the conformable fractional time derivative of order between zero and one. The solution method is a constructed ansatz that consists of linear combinations of the tan and cotan hyperbolic functions with complex coefficients. We stated clear systematic steps toward writing an exact soliton solution for the studied system. To show the efficiency of this method, we introduced some numerical examples on each obtained set of solutions. The computations showed that similar solutions can be obtained if one replaces the tan and cotan hyperbolic functions with the tan and cotan trigonometric functions. The new obtained fractional solutions could be useful in studying the broad applications of triad resonances in plasma physics and in nonlinear optics.

2

Integral solutions of nondense impulsive conformable-fractional differential equations with nonlocal condition

Bouaouid Mohamed, Hilal Khalid, Hannabou Mohamed

Journal of Applied Analysis

|

2021

|

Vol. 27, nr 2

187--197

EN

In this paper, a class of nondense impulsive differential equations with nonlocal condition in the frame of the conformable fractional derivative is studied. The abstract results concerning the existence, uniqueness and stability of the integral solution are obtained by using the extrapolation semigroup approach combined with some fixed point theorems.

3

Stability analysis of conformable fractional-order nonlinear systems depending on a parameter

Naifar O., Rebiai G., Makhlouf A., Hammami M. A., Guezane-Lakoud A.

Journal of Applied Analysis

|

2020

|

Vol. 26, nr 2

287--296

EN

In this paper, the stability of conformable fractional-order nonlinear systems depending on a parameter is presented and described. Furthermore, The design of a feedback controller for the same class of conformable fractional-order systems is introduced. Illustrative examples are given at the end of the paper to show the effectiveness of the proposed results.

4

Conformable fractional Iyengar type inequalities

Anastassiou George A.

Fasciculi Mathematici

|

2020

|

nr 63

5--21

EN

Here we present Conformable fractional Iyengar type inequalities with respect to Lp norms, with 1 < p ≤ ∞. The method is based on the right and left Conformable fractional Taylor’s formulae.

5

Analysis of positive linear continuous-time systems using the conformable derivative

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

|

2018

|

Vol. 28, no. 2

335--340

EN

Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.

6

Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo

Piotrowska E.

Archives of Electrical Engineering

|

2018

|

Vol. 67, nr 3

629–-639

EN

The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.

7

A study of critical point instability of micro and nano beams under a distributed variable-pressure force in the framework of the inhomogeneous non-linear nonlocal theory

Rahimi Z., Rezazadeh G., Sumelka W., Yang X.-J.

Archives of Mechanics

|

2017

|

Vol. 69, nr 6

413--433

EN

Fractional derivative models (FDMs) result from introduction of fractional derivatives (FDs) into the governing equations of the differential operator type of linear solid materials. FDMs are more general than those of integer derivative models (IDMs) so they are more fixable to describe physical phenomena. In this paper the inhomogeneous nonlocal theory has been introduced based on conformable fractional derivatives (CFD) to study the critical point instability of micro/nano beams under a distributed variable-pressure force. The phase of distributed variable-pressure force is used for electrostatic force, electromagnetic force and so on. This model has two free parameters: i) parameter to control the order of inhomogeneity in constitutive relations that gives a general form to the model, and ii) a nonlocal parameter to consider size dependence effects in micron and sub-micron scales. As a case study the theory has been used to model micro cantilever (C-F) and doubly-clamped (C-C) silicon beams under a distributed uniform electrostatic force in the presence of von-Karman nonlinearity and their static critical point (static pull-in instability), moreover, effects of different inhomogeneity have been shown on the pull-in instability.