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Browsing by Author "Rostamy, Davood"

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    Article
    Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices
    (Sage Publications LTD, 2013) Baleanu, Dumitru; Rostamy, Davood; Baleanu, Dumitru; 56389
    In this paper, we present a method for solving multi-dimensional fractional optimal control problems. Firstly, we derive the Bernstein polynomials operational matrix for the fractional derivative in the Caputo sense, which has not been done before. The main characteristic behind the approach using this technique is that it reduces the problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The results obtained are in good agreement with the existing ones in the open literature and it is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach 1.
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    Article
    Solving multi-term orders fractional differential equations by operational matrices of BPs with convergence analysis
    (2013) Baleanu, Dumitru; Alipour, Mohsen; Jafari, Hossein; Baleanu, Dumitru; 56389
    In this paper, we present a numerical method for solving a class of fractional differential equations (FDEs). Based on Bernstein Polynomials (BPs) basis, new matrices are utilized to reduce the multi-term orders fractional differential equation to a system of algebraic equations. Convergence analysis is shown by several theorems. Illustrative examples are included to demonstrate the validity and applicability of this method.