Journal of Mathematical Analysis and Modeling

Transmuted Sushila Distribution and its application to lifetime data

Ademola A Adetunji — 2021-03-29

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.

Bernstein polynomial induced two step hybrid numerical scheme for solution of second order initial value problems

A. O. Adeniran — 2021-03-29

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.

The Bias Estimation of Linear Regression Model with Autoregressive Scheme using Simulation Study

Sajid Ali Khan — 2021-03-29

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.

A Common Coincidence of Fixed Point for Generalized Caristi Fixed Point Theorem

Jayashree Patil — 2021-03-29

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.

Investigation of a Class of Implicit Anti-Periodic Boundary Value Problems

Laila Hashtamand — 2021-03-29

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.

Implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative

Saleh Redhwan — 2021-03-29

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.

More Properties of Fractional Proportional Differences

Thabet Abdeljawad — 2021-03-29

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.

Fixed points of $(\psi, \phi)-$contractions and Fredholm type integral equation

Nabil Mlaiki — 2021-03-29

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.