Earthline Journal of Mathematical Sciences

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EISSN : 2581-8147
Published by: Earthline Publishers (10.34198)
Total articles ≅ 226
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Merve Esra Türkay
Published: 26 September 2022
Earthline Journal of Mathematical Sciences, Volume 11, pp 145-172; https://doi.org/10.34198/ejms.11123.145172

Abstract:
$q$-Calculus Theory is rapidly growing in various directions. The goal of this paper is to collect and underline recent results on $\alpha q$-analogs of the Cesàro matrix andemphasize various generalizations. One $\alpha q$-analogs of the Cesàro matrix of order one is the triangular matrix with nonzero entries $c_{nk}^{\alpha }\left( q\right) =\tfrac{\left( \alpha q\right) ^{n-k}}{1+q+\cdots +q^{n}},\ 0\leq k\leq n$, where $\alpha ,q\in \left( 0,1\right) $. The purpose of this article examines various spectral decompositions of $C_{q}^{\alpha }=\left( c_{nk}^{\alpha }\left( q\right) \right) $ such as the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum on the sequence space $c$.
Christian John Etwire, Ibrahim Yakubu Seini, Rabiu Musah, Oluwole Daniel Makinde
Published: 14 September 2022
Earthline Journal of Mathematical Sciences, Volume 11, pp 115-143; https://doi.org/10.34198/ejms.11123.115143

Abstract:
The effects of fluctuating temperature on Darcy-Forchheimer flow of oil-based nanofluid with activation energy and velocity slip has been analyzed. Similarity transformation was used to transform the governing partial differential equations into coupled nonlinear ordinary differential equations and solved numerically with the aid of the fourth order Runge-Kutta algorithm with a shooting technique. Results for the embedded parameters controlling the flow dynamics have been tabulated and illustrated graphically. The slip velocity parameter was found to enhance the Nusselt number but depleted both the skin friction coefficient and Sherwood number while the local inertial was noted to increase both the skin friction coefficient and Sherwood number but diminishes the Nusselt number. These results indicate that the velocity slip parameter and local inertial coefficient can be used to control flow characteristics in industrial and engineering systems.
Yüksel Soykan
Published: 9 September 2022
Earthline Journal of Mathematical Sciences, Volume 11, pp 23-114; https://doi.org/10.34198/ejms.11123.23114

Abstract:
In this paper, we investigate the generalized Fibonacci (Horadam) polynomials and we deal with, in detail, two special cases which we call them $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomials. We present Binet's formulas, generating functions, Simson's formulas, and the summation formulas for these polynomial sequences. Moreover, we give some identities and matrices associated with these sequences. Finally, we present several expressions and combinatorial results of the generalized Fibonacci polynomials.
Innocent U. Akata, Festus C. Opone, Francis E. U. Osagiede
Published: 8 September 2022
Earthline Journal of Mathematical Sciences, Volume 11, pp 1-22; https://doi.org/10.34198/ejms.11123.122

Abstract:
This paper presents a new generalized bounded distribution called the Kumaraswamy unit-Gompertz (KUG) distribution. Some of the Mathematical properties which include; the density function, cumulative distribution function, survival and hazard rate functions, quantile, mode, median, moment, moment generating function, Renyi entropy and distribution of order statistics are derived. We employ the maximum likelihood estimation method to estimate the unknown parameters of the proposed KUG distribution. A Monte Carlo simulation study is carried out to investigate the performance of the maximum likelihood estimates of the unknown parameters of the proposed distribution. Two real datasets are used to illustrate the applicability of the proposed KUG distribution in lifetime data analysis.
Gbeminiyi M. Sobamowo
Published: 7 September 2022
Earthline Journal of Mathematical Sciences, Volume 10, pp 439-456; https://doi.org/10.34198/ejms.10222.439456

Abstract:
In this work, Black-Scholes differential equation for barrier/traditional option is solved using partial Taylor series expansion method. The developed solutions are in very good agreement with the closed-form solutions of the Black Scholes equation for the powered ML-payoff functions. Also, the analytical solutions of the new method in this present study give the same expressions as the solutions of projected differential equations and homotopy perturbation method as presented in the literature. Moreover, the reliability, speed, accuracy, and ease of application of the proposed method show its potential for wide areas of applications in science, financial mathematics, and engineering.
Ayokunle John Tadema, Ebenezer Olayinka Adeniyi
Published: 1 September 2022
Earthline Journal of Mathematical Sciences, Volume 10, pp 423-438; https://doi.org/10.34198/ejms.10222.423438

Abstract:
This study employed Lyapunov function method to investigate the stability of nonlinear ordinary differential equations. Using Lyapunov direct method, we constructed Lyapunov function to investigate the stability of sixth order nonlinear ordinary differential equations. We find $ V(x) $, a quadratic form, positive definite and $ U(x) $ which is also positive definite was chosen such that the derivative of $ V(x) $ with respect to time was equal to the negative value of $ U(x) $.
J. B. Omosowon, A. Y. Akinyele, B. M. Ahmed, O. Y. Saka-Balogun
Earthline Journal of Mathematical Sciences, Volume 10, pp 409-421; https://doi.org/10.34198/ejms.10222.409421

Abstract:
In this paper, results of $\omega$-order preserving partial contraction mapping generating a quasilinear equation of evolution were presented. In general, the study of quasilinear initial value problems is quite complicated. For the sake of simplicity we restricted this study to the mild solution of the initial value problem of a quasilinear equation of evolution. We show that if the problem has a unique mild solution $v\in C([0,T]: X)$ for every given $u\in C([0,T]:X)$, then it defines a mapping $u\to v=F(u)$ of $C([0,T]:X)$ into itself. We also show that under the suitable condition, there exists always a $T',\ 0<T'\leq T$ such that the restriction of the mapping $F$ to $C([0,T']:X)$ is a contraction which maps some ball of $C([0,t']:X)$ into itself by proving the existence of a local mild solution of the initial value problem.
Christophe Chesneau, Festus C. Opone, Ngozi O. Ubaka
Earthline Journal of Mathematical Sciences, Volume 10, pp 385-407; https://doi.org/10.34198/ejms.10222.385407

Abstract:
Modern applied statistics naturally give rise to the continuous Bernoulli distribution (data fitting, deep learning, computer vision, etc). On the mathematical side, it can be viewed as a one-parameter distribution corresponding to a special exponential distribution restricted to the unit interval. As a matter of fact, manageable extensions of this distribution have great potential in the same fields. In this study, we motivate a transmuted version of the continuous Bernoulli distribution with the goal of analyzing proportional data sets. The feature of the created transmuted continuous Bernoulli distribution is an additional parameter that realizes a linear tradeoff between the min and max of two continuous random variables with the continuous Bernoulli distribution. The standard study process is respected: we derive some mathematical properties of the proposed distribution and adopt the maximum likelihood estimation technique in estimating the unknown parameters involved. A Monte Carlo simulation exercise was conducted to examine and confirm the asymptotic behavior of the obtained estimates. In order to show the applicability of the proposed distribution, three proportional data sets are analyzed and the results obtained are compared with competitive distributions. Empirical findings reveal that the transmuted continuous Bernoulli distribution promises more flexibility in fitting proportional data sets than its competitors.
Timilehin Gideon Shaba, Dere Zainab Olabisi
Earthline Journal of Mathematical Sciences, Volume 10, pp 365-384; https://doi.org/10.34198/ejms.10222.365384

Abstract:
The solutions provided in this work address the classic but still relevant topic of establishing new classes of univalent functions linked to $q$-Chebyshev polynomials and examining coefficient estimates features. Aspects of quantum calculus are also considered in this research to make it more unique and produce more pleasing outcomes. We introduce new classes of univalent functions connected to $q$-Chebyshev polynomials, which generalize certain previously investigated classes. The link among the previously published findings and the current ones are noted. For each of the new classes, estimates for the Taylor-Maclaurin coefficients $|r_2|$ and $|r_3|$ are derived and the much-studied Fekete-Szegö functional.
Alaa Hussein Mohammed
Earthline Journal of Mathematical Sciences, Volume 10, pp 355-364; https://doi.org/10.34198/ejms.10222.355364

Abstract:
In this paper, we introduce a new class of operators on Hilbert space called (f*-Ҩ) quasi binormal operator of order ղ. We study this operator and give some of its properties.
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