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Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders

100%

Al-Issa S. , El-Sayed A. M. A.

tom Vol. 49, [Z] 2

171-177

In this paper we study the global existence of positive integrable solution for the nonlinear integral inclusion of fractional order..[formula] As an application the global existence of the solution for the initial-value problem of the arbitrary (fractional) orders differential inclusion..[formula] will be studied.

A coupled system of fractional order integral equations in reflexive Banach spaces

100%

El-Sayed A. M. A. , Hashem H. H. G.

Commentationes Mathematicae

2012

tom Vol. 52, [Z] 1

21-28

We present an existence theorem for at least one weak solution for a coupled system of integral equations of fractional order in reflexive Banach spaces relative to the weak topology.

Integrable solutions for quadratic Hammerstein and quadratic Urysohn functional integral equations

100%

El-Sayed A. M. A. , Hashem H. H. G.

Commentationes Mathematicae

2008

tom Vol. 48, [Z] 2

199-207

The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equation have been studied in [3], [6], [7] and [9]. Here We are concerning with the existence of L1 positive monotonic solutions for the quadratic Hammerstein and quadratic Urysohn functional integral equations.

On the weak solutions of a coupled system of Volterra-Stieltjes integral equations

100%

El-Sayed A. M. A. , Al-Fadel M. M. A.

Commentationes Mathematicae

2017

tom Vol 57, No. 2

143--151

We present an existence theorem for at least one weak solution to a coupled system of Volterra-Stieltjes integral equations in a reflexive Banach space.

On an operator functional equation in L1 [0, ∞) and Volterra-Fredholm type integral equations

80%

El-Sayed A. M. A. , Sherif N. , El-Farag I. A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2003

tom [Z] 43(1)

61-76

The existence of a solution of a nonlinear operator functional equation in the class of monotonic functions on the interval R+ = [0, oo) is investigated. The approach to establish the main result is based on the notion of measure of noncompactness and an associated fixed point theorem due to Darbo. A Volterra-Fredholm type integral equation arises as a particular case of the investigated nonlinear operator functional equation.

Continuous solutions of some fractional order integral equations

80%

Salem H. A. H. , El-Sayed A. M. A. , Moustafa O. L.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2002

tom [Z] 42(2)

209-220

In this paper, Schauder fixed point theorem is used to prove an existence of positive continuous solutions for the nonlinear fractional order integral equation x(t) = h(t) + λ Iα (ƒ(x(t)) + g(x(t))), t ϵ [0, 1], α > 0 (E), where ƒ and g are nonlinear continuous functions and ƒ is nondecreasing while g is nonincreasing. Also the existence of maximal and minimal solutions of (E) will be proved. Some fractional order differential equations will be considered.

On a mixed type integral equation and fractional-order functional differential equations

80%

El-Sayed A. M. A. , Sherif N. , Ibrahim I. A.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

tom Vol. 45, [Z] 2

237--247

In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval [0,1].