Browsing by Author "Belghaba, Kacem"

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Citation Count: Ziane, Djelloul...et al. (2019). "An Efficient Algorithm for Solving Nonlinear Systems of Partial Differential Equations with Local Fractional Operators", Punjab Unıversity Journal of Mathematics, Vol. 51, No. 9, pp. 85-99.
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 Mohamed; 56389
The 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.
Citation Count: Ziane, Djelloul...et al. (2020). "Exact Solution for Nonlinear Local Fractional Partial Differential Equations", Journal of Applied and Computational Mechanics, Vol. 6, No. 2, pp. 200-208.
Exact Solution for Nonlinear Local Fractional Partial Differential Equations
(2020) Ziane, Djelloul; Cherif, Mountassir Hamdi; Baleanu, Dumitru; Belghaba, Kacem; 56389
In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples and the results obtained, showed the flexibility of applying this algorithm, and therefore, it can be applied to similar examples.
Citation Count: Ziane, D...et al. (2019). "Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative", Journal of King Saud University Science, Vol. 31, No. 1, pp. 83-88.
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 Hamdi; 56389
In 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.
Citation Count: Ziane, Djelloul...et al. (2020). "Non-Differentiable Solution of Nonlinear Biological Population Model on Cantor Sets", Fractal and Fractional, Vol. 4, No. 1.
Non-Differentiable Solution of Nonlinear Biological Population Model on Cantor Sets
(2020) Ziane, Djelloul; Cherif, Mountassir Hamd; Baleanu, Dumitru; Belghaba, Kacem; 56389
The main objective of this study is to apply the local fractional homotopy analysis method (LFHAM) to obtain the non-differentiable solution of two nonlinear partial differential equations of the biological population model on Cantor sets. The derivative operator are taken in the local fractional sense. Two examples have been presented showing the effectiveness of this method in solving this model on Cantor sets.