JOURNAL OF ADVANCES IN MATHEMATICS KHALSA PUBLICATIONS en-US JOURNAL OF ADVANCES IN MATHEMATICS 2347-1921 <p><a href="" rel="license"><img src="" alt="Creative Commons License" /></a> All articles published in <em>Journal of Advances in Linguistics</em> are licensed under a <a href="">Creative Commons Attribution 4.0 International License</a>.</p> On the existence of continuous solutions of a nonlinear quadratic fractional integral equation <p>We prove an existence theorem for a nonlinear quadratic integral equation of fractional order, in the Banach space of real functions defined and continuous on a closed interval. This equation contains as a special case numerous integral equation studied by other authors. Finally, we give an example for indicating the natural realizations of our abstract result presented in this paper.</p> Wagdy G. El-Sayed Mahmoud M. El-Borai Mohamed M.A. metwali Nagwa I. Shemais Copyright (c) 2020 Wagdy G. El-Sayed, Mahmoud M. El-Borai, Mohamed M.A. metwali, Nagwa I. Shemais 2020-07-28 2020-07-28 19 14 25 10.24297/jam.v19i.8802 A Modern Technique for Evaluating the Square Root of a Complex Number <p>The subject of complex numbers issue is very significant because of its wide utility, especially in the engineering circuits representation. In this paper, a modern method to find the square root of the complex number has been analyzed, and some examples on the subject were presented.</p> Ahmed A. Almoselmawy Copyright (c) 2020 Ahmed A. Almoselmawy 2020-07-28 2020-07-28 19 11 13 10.24297/jam.v19i.8793 Modified New Iterative Method for Solving Nonlinear Partial Differential Equations <p>In this paper, the iterative method, proposed by Gejji and Jafari in 2006, has been modified for solving nonlinear initial value problems. The Laplace transform was used in this modification to eliminate the linear differential operator in the differential equation. The convergence of the solution was discussed according to the modification proposed. To illustrate this modification some examples were presented.</p> Alaa K. Jabber Copyright (c) 2020 Alaa K. Jabber 2020-07-28 2020-07-28 19 1 10 10.24297/jam.v19i.8800