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Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Access Right: Open AccessSubject: search.filters.subject.Local Fractional Derivative

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Now showing 1 - 9 of 9
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Nonlinear Singular P-Laplacian Boundary Value Problems in the Frame of Conformable Derivative
    (Amer inst Mathematical Sciences-aims, 2021) Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; Bouloudene, Mokhtar; Alqudah, Manar A.
    This paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations
    (Mdpi, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet Giyas; Acan, Omer
    In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.
  • Article
    Citation - WoS: 32
    A New Numerical Technique for Local Fractional Diffusion Equation in Fractal Heat Transfer
    (int Scientific Research Publications, 2016) Tenreiro Machado, J. A.; Baleanu, Dumitru; Gao, Feng; Yang, Xiao-Jun
    In this paper, a new numerical approach, embedding the differential transform (DT) and Laplace transform (LT), is firstly proposed. It is considered in the local fractional derivative operator for obtaining the non-differential solution for diffusion equation in fractal heat transfer. (C) 2016 All rights reserved.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 16
    On Local Fractional Operators View of Computational Complexity Diffusion and Relaxation Defined on Cantor Sets
    (Vinca inst Nuclear Sci, 2016) Zhang, Zhi-Zhen; Machado, J. A. Tenreiro; Yang, Xiao-Jun; Baleanu, Dumitru
    This paper treats the description of non-differentiable dynamics occurring in complex systems governed by local fractional partial differential equations. The exact solutions of diffusion and relaxation equations with Mittag-Leffler and exponential decay defined on Cantor sets are calculated. Comparative results with other versions of the local fractional derivatives are discussed.
  • Article
    Citation - WoS: 71
    Citation - Scopus: 80
    An Efficient Computational Technique for Fractal Vehicular Traffic Flow
    (Mdpi, 2018) Tchier, Fairouz; Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra
    In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.
  • Article
    Citation - WoS: 182
    Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain
    (World Scientific Publ Co Pte Ltd, 2017) Tenreiro Machado, J. A.; Baleanu, Dumitru; Yang, Xiao-Jun
    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 graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.
  • Article
    Citation - WoS: 148
    Citation - Scopus: 144
    Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets
    (Pergamon-elsevier Science Ltd, 2015) Baleanu, Dumitru; Srivastava, H. M.; Yang, Xiao-Jun
    In this letter, the local fractional similarity solution is addressed for the non-differentiable diffusion equation. Structuring the similarity transformations via the rule of the local fractional partial derivative operators, we transform the diffusive operator into a similarity ordinary differential equation. The obtained result shows the non-differentiability of the solution suitable to describe the properties and behaviors of the fractal content. (C) 2015 Published by Elsevier Ltd.
  • Conference Object
    Citation - WoS: 16
    Citation - Scopus: 16
    Observing Diffusion Problems Defined on Cantor Sets in Different Co-Ordinate Systems
    (Vinca inst Nuclear Sci, 2015) Baleanu, Dumitru; Baleanu, Mihaela-Cristina; Yang, Xiao-Jun
    In this paper, the 2-D and 3-D diffusions defined on Cantor sets with local fractional differential operator were discussed in different co-ordinate systems. The 2-D diffusion in Cantorian co-ordinate system can be converted into the symmetric diffusion defined on Cantor sets. The 3-D diffusions in Cantorian co-ordinate system can be observed in the Cantor-type cylindrical and spherical co-ordinate methods.
  • Conference Object
    Citation - WoS: 16
    Citation - Scopus: 15
    A New Numerical Technique for Solving Fractional Sub-Diffusion and Reaction Sub-Diffusion Equations With A Non-Linear Source Term
    (Vinca inst Nuclear Sci, 2015) Baleanu, Dumitru; Mallawi, Fouad; Bhrawy, Ali H.
    In this paper, we are concerned with the fractional sub-diffusion equation with a non-linear source term. The Legendre spectral collocation method is introduced together with the operational matrix of fractional derivatives (described in the Caputo sense) to solve the fractional sub-diffusion equation with a non-linear source term. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. In addition, the Legendre spectral collocation methods applied also for a solution of the fractional reaction sub-diffusion equation with a non-linear source term. For confirming the validity and accuracy of the numerical scheme proposed, two numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.