nondifferentiable functions
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2020 ◽  
Vol 25 (3) ◽  
pp. 16-25
Author(s):  
R. Pashchenko ◽  
◽  
Ivanov. Ivanov ◽  
D. Tsyupak ◽  
◽  
...  


2020 ◽  
Vol 217 (1) ◽  
pp. 161-175
Author(s):  
Toru Kitagawa ◽  
José Luis Montiel Olea ◽  
Jonathan Payne ◽  
Amilcar Velez


2019 ◽  
Author(s):  
Amilcar Velez ◽  
Jonathan Payne ◽  
Jose Luis Montiel Olea ◽  
Toru Kitagawa




Author(s):  
Toru Kitagawa ◽  
Jonathan Payne ◽  
Jose Luis Montiel Olea


Fractals ◽  
2017 ◽  
Vol 25 (05) ◽  
pp. 1750048 ◽  
Author(s):  
Y. S. LIANG

The present paper mainly investigates the definition and classification of one-dimensional continuous functions on closed intervals. Continuous functions can be classified as differentiable functions and nondifferentiable functions. All differentiable functions are of bounded variation. Nondifferentiable functions are composed of bounded variation functions and unbounded variation functions. Fractal dimension of all bounded variation continuous functions is 1. One-dimensional unbounded variation continuous functions may have finite unbounded variation points or infinite unbounded variation points. Number of unbounded variation points of one-dimensional unbounded variation continuous functions maybe infinite and countable or uncountable. Certain examples of different one-dimensional continuous functions have been given in this paper. Thus, one-dimensional continuous functions are composed of differentiable functions, nondifferentiable continuous functions of bounded variation, continuous functions with finite unbounded variation points, continuous functions with infinite but countable unbounded variation points and continuous functions with uncountable unbounded variation points. In the end of the paper, we give an example of one-dimensional continuous function which is of unbounded variation everywhere.



2016 ◽  
Author(s):  
Toru Kitagawa ◽  
Jonathan Payne ◽  
Jose Luis Montiel Olea


2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li Chen ◽  
Yang Zhao ◽  
Hossein Jafari ◽  
J. A. Tenreiro Machado ◽  
Xiao-Jun Yang

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.



2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Shu Xu ◽  
Xiang Ling ◽  
Carlo Cattani ◽  
Gong-Nan Xie ◽  
Xiao-Jun Yang ◽  
...  

The local fractional Laplace variational iteration method is used for solving the nonhomogeneous heat equations arising in the fractal heat flow. The approximate solutions are nondifferentiable functions and their plots are also given to show the accuracy and efficiency to implement the previous method.



2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Meng Li ◽  
Xiao-Feng Hui ◽  
Carlo Cattani ◽  
Xiao-Jun Yang ◽  
Yang Zhao

We investigate the local fractional linear transport equations arising in fractal porous media by using the local fractional variational iteration method. Their approximate solutions within the nondifferentiable functions are obtained and their graphs are also shown.



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