Journal of Mathematical Analysis and Modeling https://sabapub.com/index.php/jmam <p>Journal of Mathematical Analysis and Modeling (JMAM) is a peer-reviewed international journal published by Saba Publishing. <em>JMAM</em> is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.<br />JMAM is an open-access journal, which provides free access to its articles to anyone, anywhere!<br />All contributions to JMAM are published free of charge and there is no article submission charge.</p> <p><strong>Editor in Chief: Dr. <a title="Mohammed S. Abdo" href="https://www.scopus.com/authid/detail.uri?authorId=57204354133" target="_blank" rel="noopener">Mohammed S. Abdo</a></strong><br /><strong>ISSN (online)</strong>: <a href="https://portal.issn.org/resource/ISSN/2709-5924" target="_blank" rel="noopener">2709-5924</a><br /><strong>Frequency:</strong> Quarterly</p> SABA en-US Journal of Mathematical Analysis and Modeling 2709-5924 Transmuted Sushila Distribution and its application to lifetime data https://sabapub.com/index.php/jmam/article/view/127 <p>The Sushila distribution is generalized in this article using the quadratic rank transmutation map as developed by Shaw and Buckley (2007). The newly developed distribution is called the Transmuted Sushila distribution (TSD). Various mathematical properties of the distribution are obtained. Real lifetime data is used to compare the performance of the new distribution with other related distributions. The results shown by the new distribution perform creditably well.</p> Ademola A Adetunji Copyright (c) 2021 Journal of Mathematical Analysis and Modeling https://creativecommons.org/licenses/by/4.0 2021-03-29 2021-03-29 2 1 1 14 10.48185/jmam.v2i1.127 Bernstein polynomial induced two step hybrid numerical scheme for solution of second order initial value problems https://sabapub.com/index.php/jmam/article/view/128 <p>This paper presents a two-step hybrid numerical scheme with one off-grid point for the numerical solution of general second-order initial value problems without reducing to two systems of the first order. The scheme is developed using the collocation and interpolation technique invoked on Bernstein polynomial. The proposed scheme is consistent, zero stable, and is of order four($4$). The developed scheme can estimate the approximate solutions at both steps and off-step points simultaneously using variable step size. Numerical results obtained in this paper show the efficiency of the proposed scheme over some existing methods of the same and higher orders.</p> A. O. Adeniran Longe Idowu O. Edaogbogun Kikelomo Copyright (c) 2021 Journal of Mathematical Analysis and Modeling https://creativecommons.org/licenses/by/4.0 2021-03-29 2021-03-29 2 1 15 25 10.48185/jmam.v2i1.128 The Bias Estimation of Linear Regression Model with Autoregressive Scheme using Simulation Study https://sabapub.com/index.php/jmam/article/view/131 <p>In regression modeling, first-order auto correlated errors are often a problem, when the data also suffers from independent variables. Generalized Least Squares (GLS) estimation is no longer the best alternative to Ordinary Least Squares (OLS). The Monte Carlo simulation illustrates that regression estimation using data transformed according to the GLS method provides estimates of the regression coefficients which are superior to OLS estimates. In GLS, we observe that in sample size $200$ and $\sigma$=3 with correlation level $0.90$ the bias of GLS $\beta_0$ is $-0.1737$, which is less than all bias estimates, and in sample size $200$ and $\sigma=1$ with correlation level $0.90$ the bias of GLS $\beta_0$ is $8.6802$, which is maximum in all levels. Similarly minimum and maximum bias values of OLS and GLS of $\beta_1$ are $-0.0816$, $-7.6101$ and $0.1371$, $0.1383$ respectively. The average values of parameters of the OLS and GLS estimation with different size of sample and correlation levels are estimated. It is found that for large samples both methods give similar results but for small sample size GLS is best fitted as compared to OLS.</p> Sajid Ali Khan Sayyad Khurshid Shabnam Arshad Owais Mushtaq Copyright (c) 2021 Journal of Mathematical Analysis and Modeling https://creativecommons.org/licenses/by/4.0 2021-03-29 2021-03-29 2 1 26 39 10.48185/jmam.v2i1.131 A Common Coincidence of Fixed Point for Generalized Caristi Fixed Point Theorem https://sabapub.com/index.php/jmam/article/view/151 <p>In this paper, the interpolative Caristi type weakly compatible contractive in a complete metric space is applied to show some common fixed points results related to such mappings. Our application shows that the function which is used to prove the obtained results is a bounded map. An example is provided to show the useability of the acquired results.</p> Jayashree Patil Basel Hardan Amol Bachhav Copyright (c) 2021 Journal of Mathematical Analysis and Modeling https://creativecommons.org/licenses/by/4.0 2021-03-29 2021-03-29 2 1 40 46 10.48185/jmam.v2i1.151 Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems https://sabapub.com/index.php/jmam/article/view/169 <p>This research is devoted to studying a class of implicit fractional order differential equations ($\mathrm{FODEs}$) under anti-periodic boundary conditions ($\mathrm{APBCs}$). With the help of classical fixed point theory due to $\mathrm{Schauder}$ and $\mathrm{Banach}$, we derive some adequate results about the existence of at least one solution. Moreover, this manuscript discusses the concept of stability results including Ulam-Hyers (HU) stability, generalized Hyers-Ulam (GHU) stability, Hyers-Ulam Rassias (HUR) stability, and generalized Hyers-Ulam- Rassias (GHUR)stability. Finally, we give three examples to illustrate our results.</p> Laila Hashtamand Copyright (c) 2021 Journal of Mathematical Analysis and Modeling https://creativecommons.org/licenses/by/4.0 2021-03-29 2021-03-29 2 1 47 61 10.48185/jmam.v2i1.169 Implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative https://sabapub.com/index.php/jmam/article/view/176 <p>This article deals with a nonlinear implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative. The existence and uniqueness results are obtained by using the fixed point theorems of Krasnoselskii and Banach. Further, to demonstrate the effectiveness of the main results, suitable examples are granted.</p> Saleh Redhwan Sadikali L. Shaikh Copyright (c) 2021 Journal of Mathematical Analysis and Modeling https://creativecommons.org/licenses/by/4.0 2021-03-29 2021-03-29 2 1 62 71 10.48185/jmam.v2i1.176 More Properties of Fractional Proportional Differences https://sabapub.com/index.php/jmam/article/view/193 <p>The main aim of this paper is to clarify the action of the discrete Laplace transform on the fractional proportional operators. First of all, we recall the nabla fractional sums and differences and the discrete Laplace transform on a time scale equivalent to $h\mathbb{Z}$. The discrete $h-$Laplace transform and its convolution theorem are then used to study the introduced discrete fractional operators.</p> Thabet Abdeljawad Iyad Suwan Fahd Jarad Ammar Qarariyah Copyright (c) 2021 Journal of Mathematical Analysis and Modeling https://creativecommons.org/licenses/by/4.0 2021-03-29 2021-03-29 2 1 72 90 10.48185/jmam.v2i1.193 Fixed points of $(\psi, \phi)-$contractions and Fredholm type integral equation https://sabapub.com/index.php/jmam/article/view/194 <p>In this paper, we establish a fixed point theorem for controlled rectangular $b-$metric spaces for mappings that satisfy $(\psi, \phi)-$contractive mappings. Also, we give an application of our results as an integral equation.</p> Nabil Mlaiki Doaa Rizk Fatima Azmi Copyright (c) 2021 Journal of Mathematical Analysis and Modeling https://creativecommons.org/licenses/by/4.0 2021-03-29 2021-03-29 2 1 91 100 10.48185/jmam.v2i1.194