Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions(2013) Nyamoradi, Nemat; Baleanu, Dumitru; Bashiri, TaherehWe consider a system of boundary value problems for fractional differential equation given by D-0+(beta)phi(p)(d(0+)(alpha)u)(t) = lambda(1)a(1)(t)f(1)(u(t), v(t)), t is an element of (0, 1), D-0+(beta)phi(P)(D(0+)(alpha)v)(t) - lambda(2)a(2)(t)f(2)(u(t), v(t)), t is an element of (0, 1), where 1 < alpha, beta <= 2, 2 < alpha + beta <= 4, lambda(1), lambda(2) are eigenvalues, subject either to the boundary conditions D(0+)(alpha)u(0) = D(0+)(alpha)u(1) = 0, u(0) = 0, D(0+)(alpha)u(1) - Sigma(m-2)(i=1)a(1i) D(0+)(beta 1)u(xi(1i)) = 0, D(0+)(alpha)v(0) = D(0+)(alpha)v(1) =0, v(0) = 0, D(0+)(beta 1)v(1) - Sigma(m-2)(i=1)a(2i)D(0+)(beta 1)v(xi(2i)) = 0 or D(0+)(alpha)u(0) = D(0+)(alpha)u(1) = 0, u(0) = 0, D(0+)(beta 1)u(1) - Sigma(m-2)(i=1)a(1i)D(0+)(beta 1)u(xi(1i)) = psi(1)(u), D(0+)(alpha)v(0) = D(0+)(alpha)v(1) = 0, v(0) = 0, D(0+)(beta 1)v(1) - Sigma(m-2)(i=1)a(2i) D(0+)(beta 1)v(xi(2i)) = psi(2)(v) where 0 < beta(1) < 1, alpha - beta(1) - 1 > 0 and psi(1), psi(2) : C([0, 1]) -> [0, infinity) are continuous functions. The Krasnoselskiis fixed point theorem is applied to prove the existence of at least one positive solution for both fractional boundary value problems. As an application, an example is given to demonstrate some of main results.Article A k-Dimensional System of Fractional Finite Difference Equations(Hindawi Ltd, 2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, SaeidWe investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.Article A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions(Hindawi LTD, 2014) Wang, Guotao; Liu, Sanyang; Zhang, Lihong; Baleanu, DumitruA new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.