Displaying similar documents to “Harmonic Analysis on n-Dimensional Vector Spaces over Local Fields. I. Basic Results on Fractional Integration.”

A remark on local fractional calculus and ordinary derivatives

Ricardo Almeida, Małgorzata Guzowska, Tatiana Odzijewicz (2016)

Open Mathematics

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In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators

Jamshad Ahmad, Syed Tauseef Mohyud-Din, H. M. Srivastava, Xiao-Jun Yang (2015)

Waves, Wavelets and Fractals

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In this paper we develop analytical solutions for the Helmholtz and Laplace equations involving local fractional derivative operators. We implement the local fractional decomposition method (LFDM) for finding the exact solutions. The iteration procedure is based upon the local fractional derivative sense. The numerical results, whichwe present in this paper, show that the methodology used provides an efficient and simple tool for solving fractal phenomena arising in mathematical physics...