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Latest Issue

Volume 13, No. 3, September 2020




A Mini Review of Dimensional Effects on Asymptotic Mean Integrated Squared Error and Efficiencies of Selected Beta Kernels

The asymptotic mean integrated squared error (AMISE) is one of the popular performance measures in density estimation. The popularity of the AMISE in kernel estimation is because of its consideration of dimensions while other performance measures are dimensionless. This error criterion comprises of two components whose contributions are determine by the bandwidth. This paper briefly discusses the effects of dimension on the performances and efficiencies of some kernel functions of the beta polynomial family using the asymptotic mean integrated squared error. The results of the study show that as the power of the kernel function increases, the AMISE increases and with decrease in the efficiency as the power and dimensions increases. Also an increase in dimensions resulted in increase in AMISE but decreases with increase in sample sizes.


I. U. Siloko
E. A. Siloko
O. Ikpotokin



JJMS, 2020, 13(3), 327-340


In this paper, we study the existence and uniqueness of solutions for fractional differential equations with fractional integral and Caputo fractional derivatives in boundary conditions. Our analysis relies on the Banach contraction principle, Schauder fixed point theorem and Krasnoselskiiís fixed point theorem.
Examples are provided to illustrate the main results.


Choukri Derbazi
Hadda Hammouche



JJMS, 2020, 13(3), 341-361


φ− Approximate Biprojective and (φ , Ψ)−Amenable Banach Algebras

We introduce and study the concept of ϕ−approximate biprojective and (ϕ, ψ)−amenable Banach algebra A, where ϕ is a continuous homomorphism on A and ψ ϵ ΦA. We show that if A is (ϕ, ψ)−amenable then there exists a bounded net (mα) in (A ⊗ą A) such that || mα ∑ ϕ(a) − ψ ◦ ϕ(a) ∑ mα || −→ 0 and ψ ◦ π(mα) ∑ ϕ(a) −→ ϕ(a) for all a ϵ A.


Zahra Ghorbani
Javad Baradaran


JJMS, 2020, 13(3), 363-377

Generalized Normal Subgroups

In this paper, we generalize the concept of normal subgroups to Nc-normal subgroups with respect to the variety of all nilpotent groups of class at most c, (c ≥ 1). We state some properties of Nc-normal subgroups. Also we determine N2-normal subgroups and N3-normal subgroups of Q4n, D2n, SD2n and Nc-normal subgroups of SL(2, F). 



F. Mahmudi
A. Gholami


JJMS, 2020, 13(3), 379-388


Fundamental Results on Systems of Fractional Differential Equations Involving Caputo-Fabrizio Fractional Derivative

In this paper, we analyze the solutions of a linear system of fractional
differential equations involving the Caputo-Fabrizio fractional derivative. We first transform the system to a equivalent system of integro-differential equations with integer derivative. We then establish a uniqueness result for the system of fractional differential equations and present a necessary condition to guarantee the existence
of a solution. Moreover, if the solution exists, the unique solution of the fractional system is obtained explicitly and is given in a closed form. Two examples are presented to illustrate the validity of the obtained results.


Mohammed Al-Refai



JJMS, 2020, 13(3), 389-399


General Method to Generate Fuzzy Equivalence Relations in Matrix Form

In this paper, new method to generate fuzzy equivalence relations in matrix form is considered, it is not easy to check fuzzy relation in matrix form if it is equivalence relation or not, and if it is transitive or not transitive. We start building fuzzy equivalence relation in matrix forms 3 ◊ 3 and 4 ◊ 4 matrices, then by using mathematical induction we will build general method that generates fuzzy equivalence relations of the form n ◊ n matrices.


M. A. Shakhatreh
T. A. Qawasmeh



JJMS, 2020, 13(3), 401-420


Acceptance Sampling Plans Based on Truncated Life Tests for the Marshall-Olkin Inverse Gamma Distribution

An acceptance sampling plans (AS) for a truncated life test is developed, when the lifetime follows the Marshall-Olkin Inverse Gamma distribution (MOIG). The minimum sample size necessary to ensure the specified mean life is obtained. Additionally, the operating characteristic function values of the proposed sampling plans and producerís risk are provided. Using the proposed model, some tables are given and the results are illustrated by numerical examples. Finally,
Numerical examples for our proposed method are illustrated as well as a real life application is demonstrated.



Mohammad Al-Talib
Mohammad Al Kadiri
Abedel-Qader Al-Masri



JJMS, 2020, 13(3), 421-438



Statistical Inference for the Lomax Distribution under Partially Accelerated Life Tests with Progressively Type-II Censoring with Binomial Removal

In this paper a step-stress Partially Accelerated Life Test (SSPALT) is
obtained for Lomax distribution under progressive Type II censoring with random removals, assuming that the number of units removed at each failure time has a binomial distribution. The maximum likelihood estimators (MLEs) are derived using the expectation-maximization  (EM) algorithm. The Confidence intervals for the model parameters are constructed. SSPALT plan is used to minimize the Generalized Asymptotic Variance (GAV) of the ML estimators of the model parameters.
We explain the performance of our procedures using a simulation study.


Roshanak Zaman
Parviz Nasiri
Ali Shadrokh




JJMS, 2020, 13(3), 439-458



A New Iterative Natural Transform Method for Solving Nonlinear Caputo Time-Fractional Partial Differential Equations

The main purpose of this paper is to present the solutions of a class of
nonlinear Caputo time-fractional partial differential equations, in particular nonlinear Caputo time-fractional wave-like equations with variable coefficients in terms of Mittag-Leffler functions by using new technique called, new iterative natural transform method (NINTM). This method introduced an efficient tool for solving these class of equations. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed method. The results obtained show that the method described by NINTM is a very simple and easy method compared to the other methods and gives the approximate solution in the form of infinite series, this series in closed form gives the corresponding exact solution of the given problem.



Ali Khalouta
Abdelouahab Kadem



JJMS, 2020, 13(3), 459-476