Results 251 to 260 of about 317,311 (293)

ON BOX DIMENSION OF HADAMARD FRACTIONAL INTEGRAL (PARTLY ANSWER FRACTAL CALCULUS CONJECTURE)

Fractals, 2022
This paper probes into change of box dimension for an arbitrary fractal continuous function after Hadamard fractional integration. For classic calculus, we know that a function’s differentiability increases one-order after integration, and decreases one ...
W. Xiao
semanticscholar   +1 more source

Fractal calculus on [0, 1]

Chaos, Solitons & Fractals, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

FRACTAL CALCULUS AND ITS APPLICATION TO EXPLANATION OF BIOMECHANISM OF POLAR BEAR HAIRS

Fractals, 2018
The polar bear hairs have special hierarchical structure with fractal dimensions of golden ratio, which endows the creature with remarkable cool prevention.
Qingli Wang, Xiangyang Shi, Ji-Huan He, Zheng-Biao Li   +3 more
semanticscholar   +1 more source

Fractal Calculus Fundamentals

2017
Many real physical processes possess “memory,” which comes as follows: time connection between the process cause, f(t), and the process effect, g(t), is not immediate, and the condition of g(t) is specified with the condition of f(t) not at the same moment but delayed. This property is called hereditary.
Anis Kharisovich Gil’mutdinov, Pyotr Arkhipovich Ushakov, Reyad El-Khazali   +2 more
openaire   +1 more source

Construction of fractal calculus

SCIENTIA SINICA Mathematica, 2015
A fractal function does not have the derivatives in Newton sense, however, it still represents some kind of motion and then certainly it has velocity (rate of change). How to construct fractal calculus in order to describe the velocity of a fractal function is a challenging and important problem.
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Fractional Calculus on Fractal Functions

2020
The words fractional calculus were born from a communication between L’Hospital and Leibniz in 1695. By denoting the nth derivative of f with respect to x as \(\frac{d^nf}{dx^n}\), Leibniz had written a letter to L’Hospital. In his letter, Leibniz assumed that n takes the value from the positive integers, i.e., \(n\in \mathbb {N}\).
Santo Banerjee, D. Easwaramoorthy, A. Gowrisankar   +2 more
openaire   +1 more source

Fractal Frenet equations for Fractal curves: a fractal calculus approach

Boletín de la Sociedad Matemática Mexicana
The formulation of Fractal Frenet equations, which are differential equations intended to characterize the geometric behavior of vector fields along fractal curves, is presented in this study. It offers a framework for calculating the length of such irregular curves by introducing a fractal analogue of arc length.
Alireza Khalili Golmankhaneh, Palle E. T. Jørgensen, Dimiter Prodanov   +2 more
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The Generic Nonlocal Fractal Calculus

2022
The generic nonlocal fractal calculus scheme have been formulated in this work. A unified derivative operator which employs an interpolated characteristic between the generic nonlocal derivative in Riemann–Liouville and Caputo senses has also been derived. For being generic, an arbitrary kernel function has been adopted.
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Fractal Calculus

2022
Alireza Khalili Golmankhaneh, Kern Welch, TMC Priyanka, A. Gowrisankar   +3 more
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PREFACE: SPECIAL ISSUE ON RECENT DEVELOPMENTS ON THE FRACTAL AND FRACTIONAL CALCULUS IN PHYSICS AND CIRCUITS AND SYSTEMS — PART II

Fractals
Fractal and fractional calculus are hot topics widely used to describe many complex phenomena in physics and circuits and systems. Thus, this special issue compiles a series of recent works on fractal and fractional calculus in physics and circuits and ...
Kang-Jia Wang, A. R. Seadawy, Devendra Kumar   +2 more
semanticscholar   +1 more source