@article {6562,
	title = {A new class of fredholm integral equations of the second kind with non symmetric kernel: solving by wavelets method},
	journal = {Boletim da Sociedade Paranaense de Matem{\'a}tica},
	volume = {39},
	number = {6},
	year = {2021},
	pages = {67-80},
	isbn = {2175-1188},
	author = {Abdelaziz Mennouni and Ramdani, Nedjem Eddine and Khaled Zennir}
}
@article {6561,
	title = {Improvement by projection for integro-differential equations},
	journal = {Mathematical Methods in the Applied Sciences},
	year = {2020},
	publisher = {Wiley Online Library},
	isbn = {0170-4214},
	author = {Abdelaziz Mennouni}
}
@article {5261,
	title = {A New Class of Fredholm Integral Equations of the Second Kind with Non Symmetric Kernel: Solving by Wavelets Method},
	journal = {Boletim da Sociedade Paranaense de Matem{\textasciiacute}atica},
	year = {2018},
	abstract = {
	In this paper, we introduce an efficient modification of the wavelets method to solve a new class of Fredholm integral equations of the second kind with non symmetric kernel. This method based on orthonormal wavelet basis, as a consequence three systems are obtained, a Toeplitz system and two systems with condition number close to 1. Since the preconditioned conjugate gradient normal equation residual (CGNR) and preconditioned conjugate gradient normal equation error (CGNE) methods are applicable, we can solve the systems in O(2n log(n)) operations, by using the fast wavelet transform and the fast Fourier transform.

},
	author = {Abdelaziz Mennouni and Nedjem-Eddine Ramdani and Khaled Zennir}
}
@article {5260,
	title = {Numerical Solution of Generalized Logarithmic Integral Equations of the Second Kind by Projections},
	journal = {Malaysian Journal of Mathematical Sciences},
	volume = {12},
	number = {3},
	year = {2018},
	pages = {349{\textendash}367},
	abstract = {
	In this work, we present a new techniques to solve the integral equations of the second kind with logarithmic kernel. First, we show the existence and uniqueness of the solution for the given problem in a Hilbert space. Next, we discuss a projection method for solving integral equations with logarithmic kernel of the second kind; the present method based on the shifted Legendre polynomials. We examine the existence of the solution for the approximate equation, and we provide a new error estimate for the numerical solutions. At the end, numerical examples are provided to illustrate the theoretical results.

},
	author = {Hasna CHEBBAH and Abdelaziz Mennouni and Nedjem-Eddine Ramdani}
}
@article {6572,
	title = {Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods},
	journal = {Mathematical Sciences},
	volume = {11},
	number = {4},
	year = {2017},
	pages = {345-357},
	publisher = {Springer},
	isbn = {2251-7456},
	author = {Abdelaziz Mennouni and Saliha Zaouia}
}
@article {6571,
	title = {Piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind in L2},
	journal = {Journal of Computational and Applied Mathematics},
	volume = {326},
	year = {2017},
	pages = {268-272},
	publisher = {Elsevier},
	isbn = {0377-0427},
	author = {Abdelaziz Mennouni}
}
@article {5264,
	title = {Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods},
	journal = {Mathematical Sciences},
	volume = {11},
	year = {2017},
	pages = {345{\textendash}357},
	abstract = {
	Three main contributions are presented in this paper. First, the septic quasi-interpolants are calculated with all their coefficients. Second, we explore the results to solve a generalized and broad class of Fredholm integral equations of the second kind. Finally, we present three degenerate kernel methods; the latter is a combination of the two previously established methods in the literature. Moreover, we provide a convergence analysis and we give new error bounds. Finally, we exhibit some numerical examples and compare them with previous results in the literature.

},
	author = {Abdelaziz Mennouni and Saliha Zaouia}
}
@article {5263,
	title = {Piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind in L2},
	journal = {Journal of Computational and Applied Mathematics},
	volume = {326},
	year = {2017},
	pages = {268-272},
	abstract = {
	In this work, we present piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind with\&nbsp;constant coefficients\&nbsp;in\&nbsp;L2([0,1],C), using a sequence of orthogonal finite rank projections. We prove the\&nbsp;existence and uniqueness theorems\&nbsp;for the Cauchy integral equation and the approximate equation, respectively. We perform the error analysis for which we give new and improved estimates for the rates of convergence. Numerical example illustrates the theoretical results.

},
	author = {Abdelaziz Mennouni}
}
@article {5262,
	title = {FINITE TIME BLOW-UP OF SOLUTIONS FOR A NONLINEAR SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS},
	journal = {Electronic Journal of Differential Equations},
	volume = {2017},
	number = {152},
	year = {2017},
	pages = {1{\textendash}15},
	author = {Abdelaziz Mennouni and Abderrahmane Youkana}
}
