Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation

Abbas, Muhammad; Iqbal, Azhar; Băleanu, Dumitru; Asad, Jihad

doi:10.3390/sym12071154

Cited by 35 publications

(16 citation statements)

References 29 publications

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“…Fractional calculus (FC), as an extension of integer-order domain, is an efficient tool for the modeling of real-world phenomena with complex physical dynamics [4][5][6][7][8]. Nowadays, a considerable number of researches illustrated that fractional-order differential equations (FDEs) can reveal complex dynamical features more accurately than ODEs [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control

Băleanu¹,

Sajjadi²,

Jajarmi³

et al. 2021

Adv Differ Equ

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100

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In this paper, we aim to analyze the complicated dynamical motion of a quarter-car suspension system with a sinusoidal road excitation force. First, we consider a new mathematical model in the form of fractional-order differential equations. In the proposed model, we apply the Caputo–Fabrizio fractional operator with exponential kernel. Then to solve the related equations, we suggest a quadratic numerical method and prove its stability and convergence. A deep investigation in the framework of time-domain response and phase-portrait shows that both the chaotic and nonchaotic behaviors of the considered system can be identified by the fractional-order mathematical model. Finally, we present a state-feedback controller and a chaos optimal control to overcome the system chaotic oscillations. Simulation results demonstrate the effectiveness of the proposed modeling and control strategies.

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Section: Introductionmentioning

confidence: 99%

On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control

Băleanu¹,

Sajjadi²,

Jajarmi³

et al. 2021

Adv Differ Equ

Self Cite

100

View full text Add to dashboard Cite

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“…The Smoothing Spline has been used in nonparametric regression analysis [1]. The Smoothing Spline can provide better results because the analysis can overcome the patterns of data that show a sharp increase and decrease, resulting in a relatively smooth curve [2]. The advantages of using the Smoothing Spline are its unique statistical properties, it enables visual interpretation, it can handle smooth data and functions, and can readily handle data that change at certain sub-intervals [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression

2021

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In daily life, mixed data patterns are often found, namely, those that change at a certain sub-interval or that follow a repeating pattern in a certain trend. To handle this kind of data, a mixed estimator of a Smoothing Spline and a Fourier Series has been developed. This paper describes a simulation study of the estimator in nonparametric regression and its implementation in the case of poor households. The minimum Generalized Cross Validation (GCV) was used in order to select the best model. The simulation study used generation data with a Uniform distribution and a random error with a symmetrical Normal distribution. The result of the simulation study shows that the larger the sample size n, the better the mixed estimator as a model of nonparametric regression for all variances. The smaller the variance, the better the model for all combinations of samples n. Very poor households are characterized predominantly in their consumption of carbohydrates compared to that of fat and protein. The results of this study suggest that the distribution of assistance to poor households is not the same, because in certain groups there are poor households that consume higher carbohydrates, and some households may consume higher fats.

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“…The theory of fractional calculus was born in early 1695 due to a very deep question raised in a letter of L'Hospital to Leibniz [12][13][14][15][16]. During a long period of time (300 years), the fractional calculus has kept the attention of top level mathematicians.…”

Section: Introductionmentioning

confidence: 99%

A fractional q-integral operator associated with a certain class of q-Bessel functions and q-generating series

2021

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This paper deals with Al-Salam fractional q-integral operator and its application to certain q-analogues of Bessel functions and power series. Al-Salam fractional q-integral operator has been applied to various types of q-Bessel functions and some power series of special type. It has been obtained for basic q-generating series, q-exponential and q-trigonometric functions as well. Various results and corollaries are provided as an application to this theory.

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Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation

Cited by 35 publications

References 29 publications

On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control

On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control

The Application of Mixed Smoothing Spline and Fourier Series Model in Nonparametric Regression

A fractional q-integral operator associated with a certain class of q-Bessel functions and q-generating series

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