Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Publisher: search.filters.publisher.Editura Academiei RomaneWoS Q: search.filters.wosQuartile.Q2

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  • Article
    Citation - WoS: 32
    Citation - Scopus: 24
    An Analytical Study of (2 + 1)-Dimensional Physical Models Embedded Entirely in Fractal Space
    (Editura Academiei Romane, 2019) Alquran, M.; Baleanu, Dumitru; Jaradat, I.; Baleanu, D.; Abdel-Muhsen, R.; Matematik
    In this article, we analytically furnish the solution of (2+1)-dimension-al fractional differential equations, with distinct fractal-memory indices in all coordinates, as a trivariate (α, β, γ)−fractional power series representation. The method is tested on several physical models with inherited memories. Moreover, a version of Taylor’s theorem in fractal three-dimensional space is presented. As a special case, the solutions of the corresponding integer-order cases are extracted by letting α, β, γ → 1, which indicates to some extent for a sequential memory. © 2019, Editura Academiei Romane. All rights reserved.
  • Article
    A Computationally Efficient Method For a Class of Fractional Variational and Optimal Control Problems Using Fractional Gegenbauer Functions
    (Editura Academiei Romane, 2018) El-Kalaawy, Ahmed A.; Doha, Eid H.; Ezz-Eldien, Samer S.; Abdelkawy, M. A.; Hafez, R. M.; Amin, A. Z. M.; Baleanu, Dumitru; Zaky, M. A.
    This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.