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Progress on Fractal Dimensions of the Weierstrass Function and Weierstrass-Type Functions
Fractal and FractionalThe Weierstrass function W(x)=∑n=1∞ancos(2πbnx) is a function that is continuous everywhere and differentiable nowhere. There are many investigations on fractal dimensions of the Weierstrass function, and the investigation of its Hausdorff dimension is ...
Yue Qiu, Yongshun Liang
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Algebraic Construction of the Sigma Function for General Weierstrass Curves
Mathematics, 2022 The Weierstrass curve X is a smooth algebraic curve determined by the Weierstrass canonical form, yr+A1(x)yr−1+A2(x)yr−2+⋯+Ar−1(x)y+Ar(x)=0, where r is a positive integer, and each Aj is a polynomial in x with a certain degree.
Jiryo Komeda +2 more
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On the inequality of weierstrass for nonlocal functionals
Journal of Inequalities and Applications, 2001 The aim of this paper is to consider the problem of extremum of the nonlocal functional, which depends on a function and its derivative with respect to at several values of .
Kamenskii GA, Zabrodina Ju P
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Rough Paths above Weierstrass Functions
Comptes Rendus. MathématiqueRough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. The fundamental observation of rough paths theory is that if one can define “iterated integrals” above a signal, then one can ...
Cellarosi, Francesco, Selk, Zachary
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A Dichotomy for the Weierstrass-type functions [PDF]
Inventiones mathematicae, 2021 For a real analytic periodic function $ϕ:\mathbb{R}\to \mathbb{R}$, an integer $b\ge 2$ and $λ\in (1/b,1)$, we prove the following dichotomy for the Weierstrass-type function $W(x)=\sum\limits_{n\ge 0}{λ^nϕ(b^nx)}$: Either $W(x)$ is real analytic, or the Hausdorff dimension of its graph is equal to $2+\log_bλ$.
Ren, Haojie, Shen, Weixiao
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Alexandria Engineering Journal, 2022 In the present paper, the improved modified extended tanh-function method is employed to get new exact traveling wave solutions for the doubly dispersive model. Several types of solutions are obtained using the proposed method.
Manar S. Ahmed +2 more
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Fractal Calculus on Fractal Interpolation Functions
Fractal and Fractional, 2021 In this paper, fractal calculus, which is called Fα-calculus, is reviewed. Fractal calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non-differentiable and non-integrable in the sense of ordinary calculus.
Arulprakash Gowrisankar +2 more
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Mathematics, 2021 In this work, we study the generalized 2D equal-width equation which arises in various fields of science. With the aid of numerous methods which includes Lie symmetry analysis, power series expansion and Weierstrass method, we produce closed-form ...
Chaudry Masood Khalique, Karabo Plaatjie
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Results in Physics, 2022 In this paper, we consider a coupled space-time fractional nonlinear Schrödinger type equation which can be used for describing nonrelativistic quantum mechanical behavior. Under the help of the fractional complex transform and the conformable fractional
Lanfang Shi, Xianchun Zhou
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Strengthened Stone-Weierstrass type theorem [PDF]
Opuscula Mathematica, 2011 The aim of the paper is to prove that if \(L\) is a linear subspace of the space \(\mathcal{C}(K)\) of all real-valued continuous functions defined on a nonempty compact Hausdorff space \(K\) such that \(\min(|f|, 1) \in L\) whenever \(f \in L\), then ...
Piotr Niemiec
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