Browsing by Author "Neamaty, Abdolali"

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On the Existence and Uniqueness of Solution of A Nonlinear Fractional Differential Equations
(Eudoxus Press, 2013) Baleanu, Dumitru; Mohammadzadeh, B.; Neamaty, Abdolali; Baleanu, Dumitru; 56389
In this paper, we investigate the existence and uniqueness of solution for fractional boundary value problem for nonlinear fractional differential equation D-0+(alpha) u(t) = f(t,u(t)), 0 < t < 1, 2 < alpha <= 3, with the integral boundary conditions {u(0) - gamma(1) u(1) = lambda(1) integral(1)(0) g(1) (s, u(s))ds, u'(0) - gamma(2)u'(1) = lambda(2) integral(1)(0) g(2) (s, u(s))ds, u ''(0) - gamma(2)u ''(1) = 0, where D-0+(alpha) denotes Caputo derivative of order alpha. by using the fixed point theory. We apply the contraction mapping principle and Krasnoselskii's fixed point theorem to obtain some new existence and uniqueness results. Two examples are given to illustrate the main results.
Population dynamic caused by war involvement via fractional derivative on time scales
(Inderscience Enterprises LTD, 2019) Baleanu, Dumitru; Baleanu, Dumitru; Neamaty, Abdolali; Agheli, Bahram; 56389
This work suggests a model for a population dynamic caused by an enemy attack to a domain of residential areas. With the help of a local non-integer order rate of change and a new structure induced on the real line, we derive a spatial discrete diffusion equation of fractional order. Then making use of the d'Alembert's change of variable we obtain a time scale which is made of union of disjoint compact intervals. These considerations lead us to a non-homogeneous second order nonlinear differential equation. The existence of a positive solution is discussed and through a numerical example the theory is illustrated.