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Browsing by Author "Cosulshci, Mirel"

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    Asymptotic integration of some nonlinear differential equations with fractional time derivative
    (IOP Publishing Ltd, 2011) Baleanu, Dumitru; Agarwal, Ravi P.; Mustafa, Octavian G.; Cosulshci, Mirel
    We establish that, under some simple integral conditions regarding the nonlinearity, the (1 + alpha)-order fractional differential equation (0)D(t)(alpha) (x') + f (t, x) = 0, t > 0, has a solution x is an element of C([0, +infinity), R) boolean AND C(1)((0, +infinity), R), with lim(t SE arrow 0) [t(1-alpha)x'(t)] is an element of R, which can be expanded asymptotically as a+bt(alpha)+O(t(alpha-1)) when t ->+infinity for given real numbers a, b. Our arguments are based on fixed point theory. Here, (0)D(t)(alpha) designates the Riemann-Liouville derivative of order alpha is an element of (0, 1)