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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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A TYPE OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR FRACTIONAL CALCULUS
Fractals, 2016Combine Chebyshev systems with fractal interpolation, certain continuous functions have been approximated by fractal interpolation functions unanimously. Local structure of these fractal interpolation functions (FIF) has been discussed. The relationship between order of Riemann–Liouville fractional calculus and Box dimension of FIF has been ...
Liang, Yong-Shun, Zhang, Qi
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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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A Tutorial Review on Fractal Spacetime and Fractional Calculus
International Journal of Theoretical Physics, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus
Entropy, 2023Airton Deppman +2 more
exaly