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5 Journal of Mathematics and Applications

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The existence of monotonic solutions of a class of quadratic integral equations of Volterra type

Karakurt Osman, Temizer Ӧmer Faruk

Journal of Mathematics and Applications

2019

Vol. 42

117--133

Using the technique associated with measure of noncompactness we prove the existence of monotonic solutions of a class of quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

Nonincreasing solutions for quadratic integral equations of Convolution type

El-Sayed W. G., Abd El-Mowla A. A. H.

Journal of Mathematics and Applications

2019

Vol. 42

95--107

We study a nonlinear quadratic integral equation of Convolution type in the Banach space of real functions defined and continuous on a bounded and closed interval. By using a suitable measure of noncompactness, we show that the integral equation has monotonic solutions.

On the existence of solutions of a perturbed functional integral equation in the space of Lebesgue integrable functions on R+

Al Sayed W., Darwish M. A.

Journal of Mathematics and Applications

2018

Vol. 41

19--27

In this paper, we investigate and study the existence of solutions for perturbed functional integral equations of convolution type using Darbo's fixed point theorem, which is associated with the measure of noncompactness in the space of Lebesgue integrable functions on R+. Finally, we offer an example to demonstrate that our abstract result is applicable.

On a cubic integral equation of Urysohn type with linear perturbation of second kind

Awad H. K., Darwish M. A., Metwali M. M. A.

Journal of Mathematics and Applications

2018

Vol. 41

29--38

In this paper, we concern by a very general cubic integral equation and we prove that this equation has a solution in C[0; 1]. We apply the measure of noncompactness introduced by Banaś and Olszowy and Darbo's fixed point theorem to establish the proof of our main result.

Nonlinear fractional differential equations with non-instantaneous impulses in Banach spaces

Benchohra M., Slimane M.

Journal of Mathematics and Applications

2018

Vol. 41

39--51

This paper is devoted to study the existence of solutions for a class of initial value problems for non-instantaneous impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Monch's fixed point theorem and the technique of measures of noncompactness.