Jordan Journal of Mathematics and Statistics

Sensitivity Analysis and RAMD Investigation of Ghee Producing Unit of Milk Plant

Monika Saini — 2025-01-29

The main aim of present investigation is to perform sensitivity analysis and reliability, availability, maintainability, and
dependability (RAMD) investigation of ghee producing entity of milk plant. The ghee producing unit comprises four components viz.
melting vats, boilers, ghee clarifier and ghee settling tank. These components configured in series structure having various types of
redundancies. All the components’ failure and repair distribution are exponentially distributed. The switch devices, repairs are perfect
and sufficient repair facilities available with system. Simple probabilistic arguments and Markov methodology is used to derive the
reliability measures od system components. Various system effectiveness characteristics of ghee producing unit and its components
are derived. The numerical behavior of system in transient state is discussed to explore the execution of organization under various
failure and repair rates. It is revealed from numerical results that system availability is 0.75403 and ghee settling tank is most sensitive
component. The results may be utilized by maintenance personnel and system designers of milk plants to improve the performance of
the plants.

On a class of Caputo modified fractional differential equations with advanced arguments

Mohammed Derhab — 2025-01-29

In this paper by using Banach’s contraction principle, we prove the existence and uniqueness of solutions for a class of
fractional differential equations with advanced arguments has a unique solution. Moreover, we give several examples illustrating the
application of our results.

Chain Structure of Intuitionistic Level Subgroups of Groups

Divya Mary Daise S — 2025-01-29

A classic result in fuzzy group theory states that level subgroups of any fuzzy subgroup of a finite group form a chain.
Here we are trying to generalise this result to the context of intuitionistic fuzzy groups. We have obtained a characterisation of groups
in which all the Intuitionistic Level Subgroups (ILSGs) of every Intuitionistic Fuzzy Subgroups (IFSGs) form chains. W e have also
precisely obtained the finite groups having this property. W e throw some insight into the cases of infinite groups also.

Central Tendency Measurements Estimation for Skew Normal Distributions Using Taylor Series Expansion and Simpson’s Rule

Shimin Zheng — 2025-01-29

This study aims to estimate central tendency measurements, including mode and median of skew normal distributions
using Taylor series expansion and Simpson’s Rule. Skew normal distributions are characterized as continuous, unimodal, and strictly
quasi-concave. Specifically, to compute the mode approximately, the derivative of the sum of the first three terms in the T aylor series
expansion is set to be zero and then the equation is solved to find the unknown and to compute the median, the definite integration of
skew normal distribution is evaluated using Simpson’s Rule. SAS macro programs are developed to verify and assess the accuracy of
these computations under different skewness levels.

Exploring Solutions for Nonlinear Fractional Differential Equations with Multiple Fractional Derivatives and Integral Boundary Conditions

Yahia Awad — 2025-01-29

This article explores solutions for boundary value problems of nonlinear fractional differential equations with fractional integral boundary conditions. The study applies Banach’s and Krasnoselskii’s fixed point theorems to establish the existence and uniqueness
of these solutions. Additionally, a practical numerical example is presented to illustrate the real-world application of the derived results.
The research contributes significantly to the comprehension of boundary value problems for nonlinear fractional differential equations
with fractional integral boundary conditions.

The wrapped Monsef Distribution with Application to Tawaf Data

M.M.E. Abd El-Monsef — 2025-01-29

Various forms of rituals based on circular motions either clockwise or anti-clockwise. Tawaf is one of the most important
rituals of the pilgrimage and refers to walk in circles around the Holy Kaabah in an anti-clockwise motion. It’s an act of devotion to bring
the pilgrim closer to Allah spiritually. In this paper, the wrapped Monsef distribution is proposed to model the direction of the pilgrims
at tawaf. The behavior of the density function with changing parameter values is investigated and expressions for its characteristic
function, trigonometric moments, and other related circular measures are derived. Maximum likelihood estimation is used to estimate
parameters. A simulation analysis is conducted to demonstrate that the resulting ML estimator is accurate. Finally, the proposed model
is tested using three real-life datasets. Its performance is compared with some wrapped distributions to examine its flexibility and it’s
found that the proposed model has the upper hand against the competitors.

Existence and Uniqueness Theorems of MultiDimensional Integro-Differential Equations with Conformable Fractional Differointegrations

Zaid A. Mohammed — 2025-01-29

The primary goal of this article is to theoretically state and demonstrate the existence of unique solutions to three different
types of multi-dimensional conformable fractional partial integro-differential equation problems. The proofs of these theorems are
based on a well-known Banach’s fixed point theorem. On the basis of the Lipschitz condition, necessary requirements are developed
that the infernal function of the integral operators must satisfy.

Ricci bi-conformal vector fields on non-reductive four-dimensional homogeneous spaces

Mahin Sohrabpour — 2025-01-29

The goal of this paper is to find the Ricci bi-conformal left invariant vector fields on the non-reductive four-dimensional
homogeneous spaces. At first, we introduce some necessary definations, then we calculate the Lie derivative of the metric and the Lie
derivative of the Ricci tensor. We classify the Ricci bi-conformal vector fields on non-reductive four-dimensional homogeneous spaces.
Finally, we show which of them are Killing vector fields.

Bayesian and E-Bayesian Estimation for The Inverted Topp-Leone Distribution Based on Progressive Type-I Censoring Data

Hiba Z. Muhammed — 2025-01-29

In this paper, Bayesian, E-Bayesian, and non-Bayesian estimations of the shape parameter of the inverted Topp-Leone
distribution are studied based on the progressive Type I censored (PT-IC) data. The maximum likelihood estimator (MLE), Bayes, and
E-Bayes estimators of the unknown parameter under the squared error loss (SEL) function, degroot loss (DL) function, and quadratic
loss (QL) function are obtained. For E-Bayes estimates, we assumed three distributions for the hyper-parameters a and b. Three types
of confidence intervals are discussed for the unknown parameter. The effectiveness of the suggested approaches is compared using a
simulated study, and for illustration, two numerical cases have been examined.

A STUDY OF INFLUENCE OF NON-UNIFORM PARAMETER ON PERISTALTIC TRANSPORT OF CARREAU FLUID THROUGH A FINITE LENGTH CHANNEL: APPLICATION TO BILE FLOW

SHIVANGI KUMARI — 2025-01-29

The present manuscript is detailed here to analyze the impact of non uniform parameter on different types of tapered
duct which has a great similarity to bile flow through narrow or wider duct. For present analysis fluid is taken as non-Newtonian,
also Carreau fluid model is taken into interest to describe the flow characteristic of non-Newtonian bile. The wall geometry of duct is
described by the sinusoidal wave propagating along the axial direction. The governing equations of motion and continuity are simplified
with the analytical approach by considering long wavelength and low Reynolds number approximation. Analytical solutions have been
calculated for velocity, pressure gradient, shear stress and pressure rise also the impact of effecting parameters such as power index,
Weissenberg number, amplitude ratio and non-uniform parameter are discussed for different types of ducts (i.e., converging duct,
diverging duct and non-tapered duct) by plotting the graphs in MATLAB R2018b software. It is found that Bile velocity is captured
maximum in case of converging duct. Also, for Newtonian bile i.e., n = 1 or We = 0 bile reaches to its maximum velocity also When
bile is considered as Newtonian fluid (n = 1 or We = 0) less amount of wall shear stress S
rz is noticed.

On Classes of Surfaces with a Common Special Curve

Azam Etemad Dehkordy — 2025-01-29

In recent years, many researchers have studied surfaces with common geodesic or common line of curvature in different
spaces. In this paper we give necessary and sufficient conditions for some classes of surfaces in the three dimensional Euclidean space
E^3 to have a curve as common geodesic or common line of curvature. Precisely, for a given curve, we suggest a family of surfaces
which have it as their common line of curvature or common geodesic. Moreover, we illustrate the results by examples.

Modeling The Odd Moment Exponential-G Poisson Family of Distributions With Failure Time Data

Khaoula Aidi — 2025-01-29

A univariate generalized family of continuous distributions, tentatively called the odd moment exponential-G Poisson family
of distribution, has been introduced in this article. Among various techniques, the framework of compounding has been employed to
devise the odd moment exponential-G distribution with the truncated Poisson distribution. With exponential distribution as a key model
of the new family, the resultant model has been studied in lieu with theoretical and applied way. The theoretical foundation has been set
up including definite mathematical expressions for shapes of density and hazard function, moments and related generating functions,
process of residual life and its regeneration, ordered statistics, mechanics of material expressed in stress-strength expressions, Rnyi
entropy and mean deviation among others. The estimation of the model parameters is performed by the maximum likelihood method
for complete and censored scenario. A simulation study (for un-censored and censored case) is carried out under varying sample sizes
to assess the efficacy of the model parameters. Three applications to the failure time data sets related to system reliability are used to
showcase the extensibility of the proposed family. The postulated distribution is anticipated to be adaptable enough to model data sets in circumstances where both entire (un-censored) and partial information (censored) is accessible.

Implicit Solution of Two New Models of Gohar Fractional Logistic Differential Equations

Debbouche Souheyla — 2025-01-29

Two types of logistic fractional differential equations have been studies in this work. It also presents a new fractional
derivative formula which is called the Gohar fractional derivative (GFD). The principle goal of this work is finding new solutions for
each class in an implicit representation. The method used depends on the properties of the fractional derivative and some methods of
functional analysis, as we will present our study with illustrative examples.