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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.

The solvability of functional quadratic volterra-urysohn integral equations on the half line

Metwali M. M. A.

Fasciculi Mathematici

2018

Nr 61

109--123

We study the solvability of general quadratic Volterra integral equations in the space of Lebesgue integrable functions on the half line. Using the conjunction of the technique of measures of weak noncompactness with modified Schauder fixed point principle we show that the integral equation, under certain conditions, has at least one solution. Moreover, that result generalizes several ones obtained earlier in many research papers and monographs.

On some qualitative properties of integrable solutions for Cauchy-type problem of fractional order

Metwali M. M. A.

Journal of Mathematics and Applications

2017

Vol. 40

121--p134

The paper discusses the existence of solutions for Cauchy-type problem of fractional order in the space of Lebesgue integrable functions on bounded interval. Some qualitative properties of solutions are presented such as monotonicity, uniqueness and continuous dependence on the initial data. The main tools used are measure of weak (strong) noncompactness, Darbo fixed point theorem and fractional calculus.