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Bifurcations of the time-fractional generalized coupled Hirota-Satsuma KdV system

100%
Alquran M., Al-Khaled K., Ali M., Arqub O. A.
Waves, Wavelets and Fractals
|
2017
|
tom 3
|
nr 1
31-39
EN
The Hirota-Satsuma model with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified system is analyzed analytically using a new technique called residual power series method. We observe thatwhen the value of memory index (time-fractional order) is close to zero, the solutions bifurcate and produce a wave-like pattern.
2
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Controllability criteria for time-delay fractional systems with a retarded state

86%
Sikora B.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 3
521-531
EN
The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U -controllability are established and proved. Numerical examples illustrate the obtained theoretical results.
3
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Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation

72%
Staněk S.
Open Mathematics
|
2013
|
tom 11
|
nr 3
574-593
EN
We investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives.
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