JOURNAL OF ADVANCES IN MATHEMATICS 2020-09-24T22:22:26+00:00 Editorial Office Open Journal Systems A new modified homotopy perturbation method for fractional partial differential equations with proportional delay 2020-09-24T22:22:26+00:00 Ahmad. A. H. Mtawal Sameehah. R. Alkaleeli <p>In this paper, we suggest and analyze a technique by combining the Shehu transform method and the homotopy perturbation method. This method is called the Shehu transform homotopy method (STHM). This method is used to solve the time-fractional partial differential equations (TFPDEs) with proportional delay. The fractional derivative is described in Caputo's sense. The solutions proposed in the series converge rapidly to the exact solution. Some examples are solved to show the STHM is easy to apply.</p> 2020-10-11T00:00:00+00:00 Copyright (c) 2020 Ahmad. A. H. Mtawal , Sameehah R. Alkaleeli Approximation properties For generalized S–Szasz Operators with Application 2020-07-30T04:45:41+00:00 Khalid D. Abbood <p>This work focuses on a class of positive linear operators of S–Szasz type; we establish some direct results, which include Voronovskaja type asymptotic formula for a sequence of summation–integral type, we find a recurrence relation of the -the order moment and the convergence theorem for this sequence. Finally, we give some figures.</p> 2020-09-28T00:00:00+00:00 Copyright (c) 2020 Khalid D. Abbood A Study of The Density Property in Module Theory 2020-08-24T05:42:11+00:00 Majid Mohammed Abed Fatema F. Kareem <p>In this paper, there are two main objectives. The first objective is to study the relationship between the density property and some modules in detail, for instance; semisimple and divisible modules. The Addition complement has a good relationship with the density property of the modules as this importance is highlighted by any submodule N of M has an addition complement with Rad(M)=0. The second objective is to clarify the relationship between the density property and the essential submodules with some examples. As an example of this relationship, we studied the torsion-free module and its relationship with the essential submodules in module M.</p> 2020-09-10T00:00:00+00:00 Copyright (c) 2020 Majid Mohammed Abed, Fatema F. Kareem Automorphisms of Zero Divisor Graphs of Square Radical Zero Commutative Unital Finite Rings 2020-08-01T03:56:08+00:00 Lao Hussein Mude Owino Maurice Oduor Ojiema Michael Onyango <p>There has been extensive research on the structure of zero divisors and units of commutative finite rings. However, the classification of such rings via a well-known structure of zero divisors has not been done in general. More specifically, the automorphisms of such classes of rings have not been fully characterized. In this paper, we obtain a more complete<br />illustration of the automorphisms of zero divisor graphs of finite rings in which the product of any zero divisor</p> 2020-08-24T00:00:00+00:00 Copyright (c) 2020 Lao Hussein Mude, Owino Maurice Oduor, Ojiema Michael Onyango An Estimation of Parameters For Exponentiated Burr Type XII Distribution Based on Ranked Set Sampling 2020-07-20T05:00:52+00:00 Abdallah Abdelfattah Nagwan Reyad Elshendidy <p>The aim of this paper is to estimate the parameters of exponentiated Burr type XII distribution (EBXII) based on ranked set sampling (RSS) technique, and also simple random sampling(SRS) is provided by the method of maximum likelihood. Fisher information matrix for both (SRS) and (RSS) for the unknown parameters are derived. Simulation study compared between the estimators of both methods in terms of their biases, mean square errors, and efficiencies. It is shown that the estimators based on RSS are more efficient than those of SRS.</p> 2020-08-15T00:00:00+00:00 Copyright (c) 2020 Abdallah Abdelfattah, Nagwan Reyad Elshendidy On the existence of continuous solutions of a nonlinear quadratic fractional integral equation 2020-06-28T15:16:24+00:00 Wagdy G. El-Sayed Mahmoud M. El-Borai Mohamed M.A. metwali Nagwa I. Shemais <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> 2020-07-28T00:00:00+00:00 Copyright (c) 2020 Wagdy G. El-Sayed, Mahmoud M. El-Borai, Mohamed M.A. metwali, Nagwa I. Shemais A Modern Technique for Evaluating the Square Root of a Complex Number 2020-06-19T13:16:51+00:00 Ahmed A. Almoselmawy <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> 2020-07-28T00:00:00+00:00 Copyright (c) 2020 Ahmed A. Almoselmawy Modified New Iterative Method for Solving Nonlinear Partial Differential Equations 2020-06-24T05:04:52+00:00 Alaa K. Jabber <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> 2020-07-28T00:00:00+00:00 Copyright (c) 2020 Alaa K. Jabber