Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 27Citation - Scopus: 50Approximate Analytical Solutions of Goursat Problem Within Local Fractional Operators(int Scientific Research Publications, 2016) Jassim, Hassan Kamil; Al Qurashi, Maysaa; Baleanu, DumitruThe local fractional differential transform method (LFDTM) and local fractional decomposition method (LFDM) are applied to implement the homogeneous and nonhomogeneous Goursat problem involving local fractional derivative operators. The approximate analytical solution of this problem is calculated in form of a series with easily computable components. Examples are studied in order to show the accuracy and reliability of presented methods. We demonstrate that the two approaches are very effective and convenient for finding the analytical solutions of partial differential equations with local fractional derivative operators. (C) 2016 All rights reserved.Article Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative(Elsevier Science BV, 2019) Ziane, Djelloul; Baleanu, Dumitru; Belghaba, Kacem; Cherif, Mountassir HamdiIn the paper, a combined form of the Sumudu transform method with the Adomian decomposition method in the sense of local fractional derivative, is proposed to solve fractional partial differential equations. This method is called the local fractional Sumudu decomposition method (LFSDM) and is used to describe the non-differentiable problems. It would be interesting to apply LFSDM to some well-known problems to see the benefits obtained. (C) 2017 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license.Article An Efficient Algorithm for Solving Nonlinear Systems of Partial Differential Equations with Local Fractional Operators(Univ Punjab, 2019) Ziane, Djelloul; Cherif, Mountassir Hamdi; Baleanu, Dumitru; Belghaba, Kacem; Al Qurashi, Maysaa MohamedThe aim of the present study is to extend the local fractional Sumudu decomposition method (LFSDM) to resolve nonlinear systems of partial differential equations with local fractional derivatives. The derivative operators are taken in the local fractional sense. The LFSDM method provides the solution in a rapid convergent series, which may lead the non-differentiable solution in a closed form, this makes them an appropriate method for similar problems. We have provided some examples to confirm their flexibility in solving these types of systems.Article Citation - WoS: 24Citation - Scopus: 64A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets(Mdpi, 2019) Jassim, Hassan Kamil; Baleanu, DumitruIn this paper, we apply a new technique, namely, the local fractional Laplace homotopy perturbation method (LFLHPM), on Helmholtz and coupled Helmholtz equations to obtain analytical approximate solutions. The iteration procedure is based on local fractional derivative operators (LFDOs). This method is a combination of the local fractional Laplace transform (LFLT) and the homotopy perturbation method (HPM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.