Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
نویسندگان
چکیده
In this article, we verify the existence and uniqueness of a positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form Dα 0+ x(t) + f(t, x(t)) = 0, 0 < t < 1, 2 < α ≤ 3, x(0) = x′(0) = 0, x′(1) = βx(ξ), where Dα 0+ denotes the standard Riemann-Liouville fractional derivative, 0 < ξ < 1 and 0 < β ξ < α− 1. Our analysis relies on the fixed point theorem in partially ordered sets. An illustrative example is also presented.
منابع مشابه
Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0
متن کاملExiststence and uniqueness of positive solution for a class of boundary value problem including fractional differential equation
In this paper we investigate a kind of boundary value problem involving a fractional differential equation. We study the existence of positive solutions of the problem that fractional derivative is the Reimann-Liouville fractional derivative. At first the green function is computed then it is proved that the green function is positive. We present necessary and sufficient conditions for existen...
متن کاملExistence of positive solution to a class of boundary value problems of fractional differential equations
This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...
متن کاملExistence and uniqueness of solutions for p-laplacian fractional order boundary value problems
In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.
متن کاملExistence and uniqueness of positive and nondecreasing solutions for a class of fractional boundary value problems involving the p-Laplacian operator
In this article, we investigate the existence of a solution arising from the following fractional q-difference boundary value problem by using the p-Laplacian operator: Dq (φp(Dqy(t))) + f (t, y(t)) = 0 (0 < t < 1; 0 < γ < 1; 3 < δ < 4), y(0) = (Dqy)(0) = (D 2 qy)(0) = 0, a1(Dqy)(1) + a2(Dqy)(1) = 0, a1 + |a2| = 0, D0+y(t)|t=0 = 0. We make use of such a fractional q-difference boundary value pr...
متن کامل