Browsing by Author "Nyamoradi, Nemat"
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Article Citation - WoS: 17Citation - Scopus: 19Existence and Uniqueness of Positive Solutions To Fractional Boundary Value Problems With Nonlinear Boundary Conditions(Springer, 2013) Baleanu, Dumitru; Agarwal, Ravi P.; Nyamoradi, NematIn this manuscript, we consider two problems of boundary value problems for a fractional differential equation. A fixed point theorem in partially ordered sets and a contraction mapping principle are applied to prove the existence of at least one positive solution for both fractional boundary value problems.Article Citation - WoS: 16Citation - Scopus: 18On a Multipoint Boundary Value Problem for a Fractional Order Differential Inclusion on an Infinite Interval(Hindawi Ltd, 2013) Baleanu, Dumitru; Agarwal, Ravi P.; Nyamoradi, NematWe investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusion D(0+)(alpha)u(t) + F(t,u(t),u'(t)) (sic) 0, 0 < t < +infinity,u(0) = u'(0) = 0, D(alpha-1)u(+infinity) - Sigma(m-2)(i-1) beta(i)u(xi(i)) = 0, where D-0+(alpha) is the standard Riemann-Liouville fractional derivative, 2 < alpha < 3, 0 < xi(1) < xi(2) < center dot center dot center dot < xi(m-2) < +infinity, satisfies 0 < Sigma(m-2)(i=1) beta(i)xi(alpha-1)(i) < Gamma(alpha), and F : [0, +infinity) x R x R (sic) P(R) is a set-valued map. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or nonconvex values.Article Citation - WoS: 40Citation - Scopus: 49On Stability Analysis and Existence of Positive Solutions for a General Non-Linear Fractional Differential Equations(Springer, 2020) Kumar, Anoop; Baleanu, Dumitru; Khan, Aziz; Devi, Amita; Mansour Vaezpour, S.; Bashiri, Tahereh; Vaezpour, S. Mansour; Nyamoradi, NematIn this article, we deals with the existence and uniqueness of positive solutions of general non-linear fractional differential equations (FDEs) having fractional derivative of different orders involving p-Laplacian operator. Also we investigate the Hyers-Ulam (HU) stability of solutions. For the existence result, we establish the integral form of the FDE by using the Green function and then the existence of a solution is obtained by applying Guo-Krasnoselskii's fixed point theorem. For our purpose, we also check the properties of the Green function. The uniqueness of the result is established by applying the Banach contraction mapping principle. An example is offered to ensure the validity of our results.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 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.Article Citation - WoS: 7Citation - Scopus: 7Positive Solutions To Fractional Boundary Value Problems With Nonlinear Boundary Conditions(Hindawi Ltd, 2013) Baleanu, Dumitru; Bashiri, Tahereh; Nyamoradi, NematWe 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 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 Citation - WoS: 11Citation - Scopus: 12Uniqueness and Existence of Positive Solutions for Singular Fractional Differential Equations(Texas State Univ, 2014) Nyamoradi, Nemat; Baleanu, Dumitru; Bashiri, Tahereh; Vaezpour, S. Mansour; Baleanu, Dumitru; MatematikIn 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.
