scholarly journals SIMULATION OF KINETIC CURVES OF THERMO-OXIDATIVE DESTRUCTION OF PROLIMERS USING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

2021 ◽  
Vol 07 (03) ◽  
pp. 52-62
Author(s):  
Oleq Dyshin, Ibrahim Habibov, Oleq Dyshin, Ibrahim Habibov, ◽  
Camaladdin Aslanov, Sevda Aghammadova, Irada Hasanzada Camaladdin Aslanov, Sevda Aghammadova, Irada Hasanzada
Keyword(s):  
Experimental Data ◽  
Comparative Analysis ◽  
Differential Equations ◽  
Fractional Order ◽  
Oxidation Reaction ◽  
Oxidative Destruction ◽  
Fractal Kinetics ◽  
First Order ◽  
Calculation Results ◽  
Fractional Orders

In the paper it is proposed to consider fractal kinetics equations for process of thermo-oxidative destruction of melt polymers in the form of differential equations of fractional order, equaling to fraction of reactant groups of polymer, which are not subjected to destruction, with order of reaction n > 1. Small νd characterize the autoslowed-down type of reaction, and at big νd <1 - the autoaccelerated thermooxidation type with an decreasing speed of oxidation reaction, respectively much more smaller and close to an integer derivative on time of the first order. Comparative analysis of calculation results with corresponding results obtained by differential equations of integer order and degree of their matching with experimental data is given. Keywords: Fractal analysis, thermo-oxidative destruction, auto-slow and auto-accelerated type of thermal oxidation, differential equations of type and fractional orders.

A Method of Computation for Application to Nonlinear Problems

1980 ◽  
Vol 17 (1) ◽  
pp. 77-84
Author(s):  
K. F. Browne ◽  
I. Kirkland
Keyword(s):  
Experimental Data ◽  
Differential Equations ◽  
Nonlinear Problems ◽  
The Self ◽  
Computer Programme ◽  
First Order ◽  
Non Linear ◽  
First Order Differential Equations

The solution of first-order differential equations with non-linear coefficients is assisted by a computer programme which generates sets of curves and their slopes from experimental data. An example predicts the self-excitation curves of a d.c. shunt-generator.

scholarly journals Fractional differential equation with uncertainty

2021 ◽  
Vol 23 (08) ◽  
pp. 181-185
Author(s):  
Karanveer Singh ◽  
◽  
R N Prajapati ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Fractional Order Differential Equation ◽  
First Order ◽  
Fractional Differential ◽  
First Order Differential Equations

We consider a fractional order differential equation with uncertainty and introduce the concept of solution. It goes beyond ordinary first-order differential equations and differential equations with uncertainty.

Third-Kind Chebyshev Wavelet Method for the Solution of Fractional Order Riccati Differential Equations

2019 ◽  
Vol 28 (14) ◽  
pp. 1950247 ◽  
Author(s):  
Sadiye Nergis Tural-Polat
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Riccati Differential Equations ◽  
The Third ◽  
Chebyshev Wavelet ◽  
Fractional Orders

In this paper, we derive the numerical solutions of the various fractional-order Riccati type differential equations using the third-kind Chebyshev wavelet operational matrix of fractional order integration (C3WOMFI) method. The operational matrix of fractional order integration method converts the fractional differential equations to a system of algebraic equations. The third-kind Chebyshev wavelet method provides sparse coefficient matrices, therefore the computational load involved for this method is not as severe and also the resulting method is faster. The numerical solutions agree with the exact solutions for non-fractional orders, and also the solutions for the fractional orders approach those of the integer orders as the fractional order coefficient [Formula: see text] approaches to 1.

scholarly journals The influence of the Lorenz system fractionality on its recurrensivity

2019 ◽  
Vol 252 ◽  
pp. 02006
Author(s):  
Magdalena Gregorczyk ◽  
Andrzej Rysak
Keyword(s):  
Time Series ◽  
Differential Equations ◽  
System Dynamics ◽  
Phase Diagrams ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Lorenz System ◽  
Recurrence Analysis ◽  
The Lorenz System ◽  
Fractional Orders

In this work, we investigate the recurrensivity of the Lorenz system with fractional order of derivatives occurring in its all three differential equations. Several solutions of the system for varying fractional orders of individual derivatives were calculated, which was followed by an analysis of changes in the selected recurrence quantifiers occurring due to modifications of the fractional orders {q1, q2, q3}. The results of the recurrence analysis were referred to the time series plots, phase diagrams and FFT spectra. The obtained results were finally used to examine the influence of fractional derivatives on the chaos - periodicity transition of the system dynamics.

scholarly journals RESEARCH OF RESEARCH OF νt-92 TURBULENCE MODEL FOR CALCULATING AN AXISYMMETRIC SOUND JET

2020 ◽  
Vol 4 (2) ◽  
pp. 82-90
Author(s):  
Murodil Erkinjon oglu Madaliev ◽  
◽  
Dilshod Primkulovich Navruzov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Comparative Analysis ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Calculation Results ◽  
The One ◽  
Subsonic Jet

A comparative analysis of the use of the turbulence model is carried out: the one-parameter Secundov νt-92 model on the problem of an axisymmetric subsonic jet. The calculation results are compared with experimental results on the propagation of speed, voltage, and temperature. The flow is turbulent, therefore, as a mathematical model, the system of Navier-Stokes equations averaged by Reynolds (RANS) is used. For the posed problem, a generalized stream function ψ is introduced. A comparison was made of the results of the νt-92 model with experimental data from [5] the dimensionless axial velocity from the distance to the nozzle

scholarly journals Fractional Bloch's Equations Approach to Magnetic Relaxation

2015 ◽  
Vol 37 (1) ◽  
pp. 9-22 ◽  
Author(s):  
Zenon Matuszak
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Spin System ◽  
Magnetic Relaxation ◽  
Complex Structure ◽  
Time Derivative ◽  
Rate Of Change ◽  
General Strategy ◽  
First Order ◽  
Adomian Decomposition

It is the goal of this paper to present general strategy for using fractional operators to model the magnetic relaxation in complex environments revealing time and spacial disorder. Such systems have anomalous temporal and spacial response (non-local interactions and long memory) compared to systems without disorder. The systems having no memory can be modeled by linear differential equations with constant coefficients (exponential relaxation); the differential equations governing the systems with memory are known as Fractional Order Differential Equations (FODE). The relaxation of the spin system is best described phenomenologically by so-called Bloch's equations, which detail the rate of change of the magnetization M of the spin system. The Ordinary Order Bloch's Equations (OOBE) are a set of macroscopic differential equations of the first order describing the magnetization behavior under influence of static, varying magnetic fields and relaxation. It is assumed that spins relax along the z axis and in the x-y plane at different rates, designated as R1 and R2 (R1=1/T1,R2=1/T2) respectively, but following first order kinetics. To consider heterogeneity, complex structure, and memory effects in the relaxation process the Ordinary Order Bloch's Equations were generalized to Fractional Order Bloch's Equations (FOBE) through extension of the time derivative to fractional (non-integer) order. To investigate systematically the influence of “fractionality” (power order of derivative) on the dynamics of the spin system a general approach was proposed. The OOBE and FOBE were successively solved using analytical (Laplace transform), semi-analytical (ADM - Adomian Decomposition Method) and numerical methods (Grunwald- Letnikov method for FOBE). Solutions of both OOBE and FOBE systems of equations were obtained for various sets of experimental parameters used in spin !! NMR and EPR spectroscopies. The physical meaning of the fractional relaxation in magnetic resonance is shortly discussed.

Solutions of General Fractional-Order Differential Equations by Using the Spectral Tau Method

2021 ◽  
Vol 6 (1) ◽  
pp. 7
Author(s):  
Hari Mohan Srivastava ◽  
Daba Meshesha Gusu ◽  
Pshtiwan Othman Mohammed ◽  
Gidisa Wedajo ◽  
Kamsing Nonlaopon ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Convergent Series ◽  
Initial Condition ◽  
Tau Method ◽  
Series Solutions ◽  
Fractional Order Differential Equations ◽  
Functional Argument ◽  
Fractional Orders

Here, in this article, we investigate the solution of a general family of fractional-order differential equations by using the spectral Tau method in the sense of Liouville–Caputo type fractional derivatives with a linear functional argument. We use the Chebyshev polynomials of the second kind to develop a recurrence relation subjected to a certain initial condition. The behavior of the approximate series solutions are tabulated and plotted at different values of the fractional orders ν and α. The method provides an efficient convergent series solution form with easily computable coefficients. The obtained results show that the method is remarkably effective and convenient in finding solutions of fractional-order differential equations.

scholarly journals THE MATHEMATICAL MODELLING OF LINER MOVEMENT IN A MAGNETIC COMPRESSOR: ELASTIC, LIQUID AND PLASTIC LINER MODELS COMPARISON

2012 ◽  
Vol 17 (1) ◽  
pp. 31-46 ◽  
Author(s):  
Michail Galanin ◽  
Aleksey Lototsky ◽  
Alexander Rodin
Keyword(s):  
Experimental Data ◽  
Comparative Analysis ◽  
Mathematical Modelling ◽  
Longitudinal Section ◽  
Spatial Region ◽  
Elastic Liquid ◽  
Models Comparison ◽  
Calculation Results ◽  
Plastic Liner

The paper is aimed to model the electromagnetic acceleration and braking of the liner in magnetic compressor. The 2D approach corresponding to the longitudinal section of spatial region is considered. Liquid, elastic, and plastic models of the liner are presented. The comparative analysis of calculation results for different models and their correlation with experimental data are carried out. The research of the influence of circuit parameters on liner braking is done.

scholarly journals Analytical Analysis of Fractional-Order Multi-Dimensional Dispersive Partial Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 939
Author(s):  
Shuang-Shuang Zhou ◽  
Mounirah Areshi ◽  
Praveen Agarwal ◽  
Nehad Ali Shah ◽  
Jae Dong Chung ◽  
...  
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Suggested Technique ◽  
In Series ◽  
Fractional Orders

In this paper, a novel technique called the Elzaki decomposition method has been using to solve fractional-order multi-dimensional dispersive partial differential equations. Elzaki decomposition method results for both integer and fractional orders are achieved in series form, providing a higher convergence rate to the suggested technique. Illustrative problems are defined to confirm the validity of the current technique. It is also researched that the conclusions of the fractional-order are convergent to an integer-order result. Moreover, the proposed method results are compared with the exact solution of the problems, which has confirmed that approximate solutions are convergent to the exact solution of each problem as the terms of the series increase. The accuracy of the method is examined with the help of some examples. It is shown that the proposed method is found to be reliable, efficient and easy to use for various related problems of applied science.

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