Results 261 to 270 of about 317,311 (293)
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Singular Integrals and Fractal Calculus
1997This chapter is devoted to integrals similar to the familiar divergent Cauchy integral $$\int {{{\varphi (s)} \over {s - x}}ds.} $$ (1) Such integrals are often encountered in physical applications. If the function φ(s) does not vanish at s = x then the integrand in (1) has a nonintegrable singularity at that point.
Alexander I. Saichev, Wojbor Woyczynski
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THE HADAMARD FRACTIONAL CALCULUS OF A FRACTAL FUNCTION
Fractals, 2018This paper investigates the Hadamard fractional calculus of a fractal function. It is proved that there exists some linear relationship between the order of Hadamard fractional calculus and the fractal dimension of the Weierstrass function including Box dimension, [Formula: see text]-dimension and Packing dimension.
YIPENG WU, KUI YAO, XIA ZHANG
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Numerical Heat Transfer, Part A Applications
This study introduces a novel and versatile fractal finite difference scheme designed to address unsteady flow challenges in quantum calculus over flat and oscillatory sheets.
M. Arif, K. Abodayeh, Yasir Nawaz
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This study introduces a novel and versatile fractal finite difference scheme designed to address unsteady flow challenges in quantum calculus over flat and oscillatory sheets.
M. Arif, K. Abodayeh, Yasir Nawaz
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THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS
Fractals, 1995The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation.
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Local Fractional Calculus: a Calculus for Fractal Space-Time
1999Recently, new notions such as local fractional derivatives and local fractional differential equations were introduced. Here we argue that these developments provide a possible calculus to deal with phenomena in fractal space-time. We show how the usual calculus is generalized to deal with non Lipschitz functions. We also indicate how a definition of a
Kiran M. Kolwankar, Anil D. Gangal
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Hyers–Ulam stability on local fractal calculus and radioactive decay
The European Physical Journal Special Topics, 2021Alireza Khalili Golmankhaneh +2 more
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