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- Mouffak Benchohra, Samira Hamani, +5 authors Hari M. Srivastava
- 2008

In this paper, we shall establish sufficient conditions for the existence of solutions for a first order boundary value problem for fractional differential equations. Full text

Values of λ are determined for which there exist positive solutions of the system of three-point boundary value problems, u +λa(t)f(v) = 0, v+λb(t)g(u) = 0, for 0 < t < 1, and satisfying, u(0) = βu(η), u(1) = αu(η), v(0) = βv(η), v(1) = αv(η). A Guo-Krasnosel’skii fixed point theorem is applied.

- Jessada Tariboon, Sotiris K. Ntouyas, Arisa Singubol
- J. Applied Mathematics
- 2014

In this paper we study the existence of solutions for the initial value problem for semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Leray-Schauder type is the main tool in our analysis.

In this paper, we discuss the existence of solutions for a boundary value problem of second order fractional differential inclusions with four-point integral boundary conditions involving convex and non-convex multivalued maps. Our results are based on the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory. Full… (More)

M. Benchohra, J. R. Graef, J. Henderson and S. K. Ntouyas 1 Department of Mathematics, University of Sidi Bel Abbes BP 89 2000 Sidi Bel Abbes Algeria e-mail: benchohra@yahoo.com 2 Mathematics Department, University of Tennessee at Chattanooga Chattanooga, TN 37403-2504 USA e-mail: John-Graef@utc.edu 3 Department of Mathematics, Baylor University Waco, TX… (More)

- Mouffak Benchohra, Johnny Henderson, Sotiris K. Ntouyas
- Appl. Math. Lett.
- 2002

In this paper, we first present an impulsive version of Filippov’s Theorem for first-order neutral functional differential inclusions of the form, d dt [y(t)− g(t, yt)] ∈ F (t, yt), a.e. t ∈ J\{t1, . . . , tm}, y(t+k )− y(tk ) = Ik(y(tk )), k = 1, . . . , m, y(t) = φ(t), t ∈ [−r, 0], where J = [0, b], F is a set-valued map and g is a single-valued function.… (More)

Intervals of the parameter λ are determined for which there exist positive solutions for the system of nonlinear differential equations, u(n) + λa(t)f(v) = 0, v(n)+λb(t)g(u) = 0, for 0 < t < 1, and satisfying three-point nonlocal boundary conditions, u(0) = 0, u(0) = 0, . . . , u(n−2)(0) = 0, u(1) = αu(η), v(0) = 0, v(0) = 0, . . . , v(n−2)(0) = 0, v(1) =… (More)

This paper studies a boundary value problem of nonlinear fractional differential equations of order q ∈ 1, 2 with three-point integral boundary conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameter in three-point… (More)

In this paper we prove controllability results for mild solutions defined on a compact real interval for first order differential evolution inclusions in Banach spaces with non-local conditions. By using suitable fixed point theorems we study the case when the multi-valued map has convex as well as non-convex values.