Browsing by Author "Babakhani, Azizollah"

Now showing 1 - 7 of 7

Citation - WoS: 6
Citation - Scopus: 6
A caputo fractional order boundary value problem with integral boundary conditions
(Eudoxus Press, Llc, 2013) Babakhani, Azizollah; Abdeljawad, Thabet; Matematik
In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.
Citation - WoS: 2
Citation - Scopus: 8
Employing of some basic theory for class of fractional differential equations
(Springer, 2011) Babakhani, Azizollah; Baleanu, Dumitru; Matematik
Basic theory on a class of initial value problem of some fractional differential equation involving Riemann-Liouville differential operators is discussed by employing the classical approach from the work of Lakshmikantham and A. S. Vatsala (2008). The theory of inequalities, local existence, extremal solutions, comparison result and global existence of solutions are considered. Our work employed recent literature from the work of (Lakshmikantham and A. S. Vatsala, (2008)).
Citation - WoS: 5
Citation - Scopus: 6
Existence and Uniqueness of Solution for A Class of Nonlinear Fractional Order Differential Equations
(Hindawi Ltd, 2012) Babakhani, Azizollah; Baleanu, Dumitru; 56389; Matematik
We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations (D-alpha - rho tD(beta))x(t) = f(t, x(t), D(gamma)x(t)), t is an element of (0, 1) with boundary conditions x(0) = x(0), x(1) = x(1) or satisfying the initial conditions x(0) = 0, x'(0) = 1, where D-alpha denotes Caputo fractional derivative, rho is constant, 1 < alpha < 2, and 0 < beta + gamma <= alpha. Schauder's fixed-point theorem was used to establish the existence of the solution. Banach contraction principle was used to show the uniqueness of the solution under certain conditions on f.
Citation - WoS: 6
Citation - Scopus: 6
Existence of positive solutions for a class of delay fractional differential equations with generalization to n-term
(Hindawi Ltd, 2011) Babakhani, Azizollah; Baleanu, Dumitru; Matematik
We established the existence of a positive solution of nonlinear fractional differential equations pound (D) [x(t)-x(0)] = f(t, x(t)), t. is an element of (0, b], with finite delay x (t) = omega (t), t is an element of [-tau,0], where lim(t -> 0)f(t, x(t)) = +infinity, that is, f is singular at t = 0 and x(t) is an element of C([-tau,0], R->= 0). The operator of (D) pound involves the Riemann- Liouville fractional derivatives. In this problem, the initial conditions with fractional order and some relations among them were considered. The analysis rely on the alternative of the Leray-Schauder fixed point theorem, the Banach fixed point theorem, and the Arzela- Ascoli theorem in a cone.
Citation - WoS: 5
Citation - Scopus: 5
Existence Results for a Class of Fractional Differential Equations with Periodic Boundary Value Conditions and with Delay
(Hindawi Ltd, 2013) Karami, Hadi; Babakhani, Azizollah; Baleanu, Dumitru; 56389; Matematik
We discuss the existence and uniqueness of solution for two types of fractional order ordinary and delay differential equations. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First we use Banach contraction principle to prove the uniqueness of solution and then Krasnoselskii's fixed point theorem to show the existence of the solution under certain conditions in a Banach space.
Citation - WoS: 33
Citation - Scopus: 35
Hopf bifurcation for a class of fractional differential equations with delay
(Springer, 2012) Babakhani, Azizollah; Baleanu, Dumitru; Khanbabaie, Reza; Matematik
The main purpose of this manuscript is to prove the existence of solutions for delay fractional order differential equations (FDE) at the neighborhood of its equilibrium point. After we convert the delay FDE into linear delay FDE by using its equilibrium point, we define the 1:2 resonant double Hopf point set with its characteristic equation. We find the members of this set in different cases. The bifurcation curves for a class of delay FDE are obtained within a differential operator of Caputo type with the lower terminal at -a.
Citation - WoS: 9
Citation - Scopus: 9
The Existence and Uniqueness of Solutions for A Class of Nonlinear Fractional Differential Equations With Infinite Delay
(Hindawi Ltd, 2013) Babakhani, Azizollah; Baleanu, Dumitru; Agarwal, Ravi P.; 56389; Matematik
We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem in Omega = {y : (-infinity,b] -> R : y vertical bar(<-infinity, 0]) epsilon B} such that y vertical bar ([0,b]) is continuous and B is a phase space.