The Experts below are selected from a list of 288 Experts worldwide ranked by ideXlab platform
Wei Xiao - One of the best experts on this subject based on the ideXlab platform.
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fractal dimension of riemann Liouville Fractional Integral of certain unbounded variational continuous function
Fractals, 2017Co-Authors: Yang Li, Wei XiaoAbstract:In the present paper, a one-dimensional continuous function of unbounded variation on the interval [0, 1] has been constructed. Box dimension of this function has been proved to be 1. Furthermore, Box dimension of its Riemann–Liouville Fractional Integral of any order has also been proved to be 1.
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FRACTAL DIMENSION OF RIEMANN–Liouville Fractional Integral OF CERTAIN UNBOUNDED VARIATIONAL CONTINUOUS FUNCTION
Fractals, 2017Co-Authors: Yang Li, Wei XiaoAbstract:In the present paper, a one-dimensional continuous function of unbounded variation on the interval [0, 1] has been constructed. Box dimension of this function has been proved to be 1. Furthermore, Box dimension of its Riemann–Liouville Fractional Integral of any order has also been proved to be 1.
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Fractal dimension of Fractional Integral of continuous functions
2017 29th Chinese Control And Decision Conference (CCDC), 2017Co-Authors: Junhuai Du, Wei Xiao, Yong Shun LiangAbstract:This paper mainly makes research on fractal dimension of fractal functions. We give basic estimation of fractal dimension, such as Box dimension and Hausdorff dimension, of Fractional calculus of continuous functions. For a continuous function, upper Box dimension of its Riemann-Liouville Fractional Integral of order v has been proved to be no more than 2 - v when 0 ≤ v ≤ 1. Furthermore, if a continuous function which satisfies α-Hölder condition, upper Box dimension of its Riemann-Liouville Fractional Integral is no more than 2 - α when 0 ≤ α ≤ 1. This means upper Box dimension of Riemann-Liouville Fractional Integral of a continuous function satisfying α-Hölder condition of order v is no more than min{2 - v, 2 - α} when 0 ≤ v, α ≤ 1. With method of auxiliary function, upper Box dimension of Riemann-Liouville Fractional Integral of any continuous functions satisfying α-Hölder condition of order v is strictly less than min{2 - v, 2 - α} when 0 ≤ v, α ≤ 1.
Yong Shun Liang - One of the best experts on this subject based on the ideXlab platform.
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Fractal dimension of Riemann-Liouville Fractional Integral of 1-dimensional continuous functions
Fractional Calculus and Applied Analysis, 2018Co-Authors: Yong Shun LiangAbstract:Abstract The present paper investigates fractal dimension of Fractional Integral of continuous functions whose fractal dimension is 1 on [0, 1]. For any continuous functions whose Box dimension is 1 on [0, 1], Riemann-Liouville Fractional Integral of these functions of any positive order has been proved to still be 1-dimensional continuous functions on [0, 1].
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Dimension of Riemann-Liouville Fractional Integral of Takagi function
2018 Chinese Control And Decision Conference (CCDC), 2018Co-Authors: Yong Shun LiangAbstract:In this paper, we mainly discuss the characteristics of a type of special function called Takagi function which was derived from Weierstrass function. We have proved this function is continuous but can not be differentiable on any subinterval. In other words, it has no bounded variation points even one. Then, we calculate its Hausdorff dimension and Box dimension is 1. Furthermore, its Riemann-Liouville Fractional Integral is also 1. Finally, some numerical and graphic results are provided to characterize Takagi function.
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Fractal dimension of Fractional Integral of continuous functions
2017 29th Chinese Control And Decision Conference (CCDC), 2017Co-Authors: Junhuai Du, Wei Xiao, Yong Shun LiangAbstract:This paper mainly makes research on fractal dimension of fractal functions. We give basic estimation of fractal dimension, such as Box dimension and Hausdorff dimension, of Fractional calculus of continuous functions. For a continuous function, upper Box dimension of its Riemann-Liouville Fractional Integral of order v has been proved to be no more than 2 - v when 0 ≤ v ≤ 1. Furthermore, if a continuous function which satisfies α-Hölder condition, upper Box dimension of its Riemann-Liouville Fractional Integral is no more than 2 - α when 0 ≤ α ≤ 1. This means upper Box dimension of Riemann-Liouville Fractional Integral of a continuous function satisfying α-Hölder condition of order v is no more than min{2 - v, 2 - α} when 0 ≤ v, α ≤ 1. With method of auxiliary function, upper Box dimension of Riemann-Liouville Fractional Integral of any continuous functions satisfying α-Hölder condition of order v is strictly less than min{2 - v, 2 - α} when 0 ≤ v, α ≤ 1.
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Upper Bound Estimation of Fractal Dimensions of Fractional Integral of Continuous Functions
Advances in Pure Mathematics, 2015Co-Authors: Yong Shun LiangAbstract:Fractional Integral of continuous functions has been discussed in the present paper. If the order of Riemann-Liouville Fractional Integral is v, fractal dimension of Riemann-Liouville Fractional Integral of any continuous functions on a closed interval is no more than 2 - v.
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box dimensions of riemann Liouville Fractional Integrals of continuous functions of bounded variation
Nonlinear Analysis-theory Methods & Applications, 2010Co-Authors: Yong Shun LiangAbstract:Abstract If a continuous function f ( x ) has bounded variation on the unit interval [ 0 , 1 ] , the box dimension of f ( x ) is 1. Furthermore, the box dimension of a Riemann–Liouville Fractional Integral of f ( x ) is still 1.
Yang Li - One of the best experts on this subject based on the ideXlab platform.
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fractal dimension of riemann Liouville Fractional Integral of certain unbounded variational continuous function
Fractals, 2017Co-Authors: Yang Li, Wei XiaoAbstract:In the present paper, a one-dimensional continuous function of unbounded variation on the interval [0, 1] has been constructed. Box dimension of this function has been proved to be 1. Furthermore, Box dimension of its Riemann–Liouville Fractional Integral of any order has also been proved to be 1.
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FRACTAL DIMENSION OF RIEMANN–Liouville Fractional Integral OF CERTAIN UNBOUNDED VARIATIONAL CONTINUOUS FUNCTION
Fractals, 2017Co-Authors: Yang Li, Wei XiaoAbstract:In the present paper, a one-dimensional continuous function of unbounded variation on the interval [0, 1] has been constructed. Box dimension of this function has been proved to be 1. Furthermore, Box dimension of its Riemann–Liouville Fractional Integral of any order has also been proved to be 1.
Wei Zhao - One of the best experts on this subject based on the ideXlab platform.
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composition of one dimensional continuous functions and their riemann Liouville Fractional Integral
Fractals, 2019Co-Authors: Bin Yu, Tao Zhang, Wei ZhaoAbstract:In this paper, we make research on composition of continuous functions with Box dimension one of bounded variation or unbounded variation on [0, 1]. It has been proved that one-dimensional continuo...
Mohsen Razzaghi - One of the best experts on this subject based on the ideXlab platform.
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A numerical method for Fractional pantograph differential equations based on Taylor wavelets
Transactions of the Institute of Measurement and Control, 2019Co-Authors: Panupong Vichitkunakorn, Thieu N. Vo, Mohsen RazzaghiAbstract:We present an efficient numerical method for solving Fractional pantograph differential equations by applying Taylor wavelets. We give an exact formula for the Riemann-Liouville Fractional Integral...
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Fractional-order Bessel functions with various applications
Applications of Mathematics, 2019Co-Authors: Haniye Dehestani, Yadollah Ordokhani, Mohsen RazzaghiAbstract:We introduce Fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the Fractional calculus. To calculate derivatives and Integrals, we use Caputo Fractional derivatives and Riemann-Liouville Fractional Integral definitions. Then, operational matrices of Fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error estimate between the computed approximations and the exact solution and apply it in some examples. Applications are given to three model problems to demonstrate the effectiveness of the proposed method.
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Taylor wavelet method for Fractional delay differential equations
Engineering with Computers, 2019Co-Authors: Phan Thanh Toan, Thieu N. Vo, Mohsen RazzaghiAbstract:We present a new numerical method for solving Fractional delay differential equations. The method is based on Taylor wavelets. We establish an exact formula to determine the Riemann–Liouville Fractional Integral of the Taylor wavelets. The exact formula is then applied to reduce the problem of solving a Fractional delay differential equation to the problem of solving a system of algebraic equations. Several numerical examples are presented to show the applicability and the effectiveness of this method.
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An approximate method for solving Fractional optimal control problems by hybrid functions
Journal of Vibration and Control, 2016Co-Authors: Somayeh Mashayekhi, Mohsen RazzaghiAbstract:In this paper, a new numerical method for solving Fractional optimal control problems by using hybrid functions is presented. The Riemann–Liouville Fractional Integral operator for hybrid functions...