Journal ArticleDOI
A new computational approach for solving nonlinear local fractional PDEs
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TLDR
A new factorization technique for nonlinear ODEs involving local fractional derivatives for the first time is proposed by making use of the traveling-wave transformation and the results illustrate that the proposed method is efficient and accurate for finding the exact solutions for a class of local fractionals occurring in mathematical physics.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2017-10-01. It has received 182 citations till now. The article focuses on the topics: Fractional calculus & Nonlinear system.read more
Citations
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An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma
TL;DR: In this paper, a coupling of homotopy perturbation technique and sumudu transform is presented for studying the nonlinear behavior of plasma system and highlight the important points.
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Construction of solitary wave solutions to the nonlinear modified Kortewege-de Vries dynamical equation in unmagnetized plasma via mathematical methods
TL;DR: In this paper, the propagation of one-dimensional nonlinear behavior in a unmagnetized plasma was considered and the reductive perturbation technique was used to formulate the nonlinear mathematic mod...
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On novel nondifferentiable exact solutions to local fractional Gardner's equation using an effective technique
Behzad Ghanbari,Behzad Ghanbari +1 more
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A new analysis of fractional fish farm model associated with Mittag-Leffler-type kernel
Abstract: In this paper, we analyze the dynamical behavior of fish farm model related to Atangana–Baleanu derivative of arbitrary order. The model is constituted with the group of nonlinear differential equa...
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Some new families of solitary wave solutions of the generalized Schamel equation and their applications in plasma physics
TL;DR: In this article, the authors studied analytically the propagation of nonlinear ion acoustic solitary waves modeled by the generalized Schamel (GS) equation arising in plasma physics using auxiliary equation mapping method.
References
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Journal ArticleDOI
Fractional differentiability of nowhere differentiable functions and dimensions
TL;DR: Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the critical order 2−s and not so for orders between 2 −s and 1, where s, 1
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Local Fractional Fokker-Planck Equation
TL;DR: Local fractional differential equations (LDFDE) as mentioned in this paper is a new class of differential equations, which involve local fractional derivatives and appear to be suitable to deal with phenomena taking place in fractal space and time.
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Fractional differentiability of nowhere differentiable functions and dimensions
TL;DR: It is argued that Local fractional derivatives provide a powerful tool to analyze pointwise behavior of irregular signals to show a direct connection between local fractional differentiability and the box dimension/local Holder exponent.
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Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations
TL;DR: The present methodology is shown to provide a useful approach to solve the local fractional nonlinear partial differential equations (LFNPDEs) in mathematical physics.
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No violation of the Leibniz rule. No fractional derivative
TL;DR: It is proved that all fractional derivatives D α, which satisfy the Leibniz rule D α ( fg ) = ( D α f ) g + f ( D β g ) , should have the integer order α = 1.