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1

Solvability of a Coupled System of Fractional Differential Equations with Nonlocal and Integral Boundary Conditions

Ahmad B., Ntouyas S. K., Alsaedi A., Hobiny A.

Fundamenta Informaticae

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2017

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Vol. 151, nr 1/4

91--108

EN

This paper is concerned with the existence and uniqueness of solutions for a coupled system of fractional differential equations with nonlocal and integral boundary conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. The results are explained with the aid of examples. The case of nonlocal strip conditions is also discussed.

2

On locally γ-s-closed spaces

Hussain S., Ahmad B.

Fasciculi Mathematici

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2013

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Nr 51

93--103

EN

In this paper, we aim to continue studying the properties of γ-s-closed spaces introduced and discussed in [5] and [9]. The concept of locally γ-s-closed space have been introduced. Certain important characterizations and properties of locally γ-s-closed space have also been established.

3

Boundary value problems for n-th order differential inclusions with four-point integral boundary conditions

Ahmad B., Ntouyas S. K.

Opuscula Mathematica

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2012

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Vol. 32, no. 2

205-226

EN

In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of n-th order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.

4

Stability of impulsive hybrid set-valued differential wquations with delay by perturbing lyapunov functions

Ahmad B.

Journal of Applied Analysis

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2008

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Vol. 14, nr 2

209-218

EN

We study the stability of the zero solution of an impulsive set differential system with delay by means of the perturbing Lyapunov function method. Sufficient conditions for the stability of the zero solution of impulsive set differential equations with delay are presented.

5

Extended method of quasilinearization for a nonlinear three-point boundary value problem

Ahmad B., Alsaedi A., Garout D.

Demonstratio Mathematica

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2006

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Vol. 39, nr 4

803-814

EN

In this paper, we discuss the generalized quasilinearization technique for a second order nonlinear differential equation with nonlinear three-point general boundary conditions. In fact, we obtain sequences of upper and lower solutions converging mono- tonically and quadratically to the unique solution of the nonlinear three-point boundary value problem.