Local fractional Fourier series

Yang, Xiao; Băleanu, Dumitru

doi:10.1016/b978-0-12-804002-7.00002-4

Cited by 63 publications

(17 citation statements)

References 29 publications

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“…[1][2][3][4][5][6][7][8] Recent examples are the heat transport in fractal media, 9 fractal hydrodynamic equations, 10 fractal electrostatics, 11 fractal FokkerPlanck equations 12 and fractal description of stress and strain in elasticity. 13 There are several alternative approaches for describing the complex and fractal behaviors in nature.…”

Section: Introductionmentioning

confidence: 99%

Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain

2017

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The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable ¶ Corresponding author. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. X. -J. Yang, J. A. T. Machado & D. Baleanu graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains. 1740006-1

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Section: Introductionmentioning

confidence: 99%

Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain

2017

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“…In [17]- [19], authors deduced some generalized integral inequalities which are Ostrowski and Grüss type by using local fractional integrals. Yang mentioned some topics related to local fractional calculus and its applications in [21]- [24].…”

Section: Theorem 22 (Generalized Grüss Inequalitymentioning

confidence: 99%

Some Generalized Inequalities Involving Local Fractional Integrals and their Applications for Random Variables and Numerical Integration

Erden

Sarıkaya

Çelik

2016

Journal of Applied Mathematics, Statistics and Informatics

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“…If j τ is a fractal imaginary unit and κ ∈ N 0 , then the fractal special functions defined on fractal sets 24,[38][39][40][41][43][44][45][46][47][48] are listed in Table 1, N 0 being (as usual) the set of nonnegative integers.…”

Section: Preliminaries Definitions and Fractal Special Functionsmentioning

confidence: 99%

“…[34][35][36][37] There is an alternative operator (called local FC) to model the local FODEs in fractal electric circuits, 38 free damped vibrations, 39 shallow water surfaces 40 and populations. [41][42][43] The fractal partial differential equations (FPDEs) in mathematical physics were also discussed in Refs. [44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Non-Differentiable Exact Solutions for the Nonlinear Odes Defined on Fractal Sets

2017

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In the present paper, a family of the special functions via the celebrated Mittag-Leffler function defined on the Cantor sets is investigated. The nonlinear local fractional ODEs (NLFODEs) are presented by following the rules of local fractional derivative (LFD). The exact solutions for these problems are also discussed with the aid of the non-differentiable charts on Cantor sets. The obtained results are important for describing the characteristics of the fractal special functions.

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Local fractional Fourier series

Cited by 63 publications

References 29 publications

Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain

Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain

Some Generalized Inequalities Involving Local Fractional Integrals and their Applications for Random Variables and Numerical Integration

Non-Differentiable Exact Solutions for the Nonlinear Odes Defined on Fractal Sets

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