Browsing by Author "Bashiri, Tahereh"

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Positive solutions to fractional boundary value problems with nonlinear boundary conditions
(2013) Baleanu, Dumitru; Baleanu, Dumitru; Bashiri, Tahereh; 56389; Matematik
We consider a system of boundary value problems for fractional differential equation given by D0+β φp (D 0+αu) (t) = λ1a1 (t) f1 (u (t), v (t)), t ∈ (0,1), D0+β φp (D0+αv) (t) = λ 2a2 (t) f2 (u (t), v (t)), t ∈ (0,1), where 1 < α, β ≤ 2, 2 < α + β ≤ 4, λ1,λ2 are eigenvalues, subject either to the boundary conditions D0+α u (0) = D 0+α u (1) = 0, u (0) = 0, D0+ β1 u (1) - Σi=1m-2 a1i D0+β1 u (χ1i) = 0, D0+ α v (0) = D0+α v (1) = 0, v (0) = 0, D0+β1 v (1) - Σi = 1 m-2 a2i D0+β1 v (χ2i) = 0 or D0+α u (0) = D 0+α u (1) = 0, u (0) = 0, D0+ β1 u (1) - Σi = 1m 2 a1i D0+β1 u (χ1i) = ψ1 (u), D0+α v (0) = D0+α v (1) = 0, v (0) = 0, D0+β1 v (1) - Σ i = 1 m-2 a2i D0+β1 v (χ2i) = ψ2 (v), where 0 < β1 < 1, α - β1- 1 ≥ 0 and ψ1, ψ2: C ([ 0,1 ]) → [ 0, ∞) 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.
Citation - WoS: 6
Citation - Scopus: 6
Positive Solutions To Fractional Boundary Value Problems With Nonlinear Boundary Conditions
(Hindawi Ltd, 2013) Nyamoradi, Nemat; Baleanu, Dumitru; Baleanu, Dumitru; Bashiri, Tahereh; 56389; Matematik
We 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.
Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions
(2013) Baleanu, Dumitru; Baleanu, Dumitru; Bashiri, Tahereh; 56389; Matematik
We 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.
Citation - WoS: 11
Citation - Scopus: 12
Uniqueness and existence of positive solutions forsingular fractional differential equations
(Texas State Univ, 2014) Nyamoradi, Nemat; Baleanu, Dumitru; Bashiri, Tahereh; Vaezpour, S. Mansour; Baleanu, Dumitru; 56389; Matematik
In this article, we study the existence of positive solutions for the singular fractional boundary value problem [GRAPHICS] where 1 < alpha <= 2, 0 < xi <= 1/2, a is an element of [0, infinity), 1 < alpha - delta < 2, 0 < beta(i) < 1, A, B-i, 1 <= i <= k, are real constant, D-alpha is the Reimann-Liouville fractional derivative of order alpha. By using the Banach's fixed point theorem and Leray-Schauder's alternative, the existence of positive solutions is obtained. At last, an example is given for illustration.