A fuzzy solution of nonlinear partial differential equations
OMA-Vol. 5 (2021), Issue 1, pp. 51 – 63 Open Access Full-Text PDF
Mawia Osman, Zengtai Gong, Altyeb Mohammed Mustafa
Abstract: In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. Some examples are solved to illustrate the proposed method.
Laguerre collocation method for solving higher order linear boundary value problems
EASL-Vol. 4 (2021), Issue 1, pp. 42 – 49 Open Access Full-Text PDF
Tersoo Luga, Sunday Simon Isah, Vershima Benjamin Iyorter
Abstract: Collocation methods are efficient approximate methods developed by utilizing suitable set of functions known as trial or basis functions. These methods are used for solving differential equations, integral equations and integro-differential equations, etc. In this study, the Laguerre polynomial of degree 10 is used as a basis function to propose a collocation method for solving higher order linear ordinary differential equations. Four examples on \(4th\), \(6th\), \(8th\) and \(10th\) order ordinary differential equations are selected to illustrate the effectiveness of the method. The numerical results show that the proposed collocation method is easy and straightforward to implement, nevertheless, it is very accurate.
Deutsch paths and their enumeration
ODAM-Vol. 4 (2021), Issue 1, pp. 12 – 18 Open Access Full-Text PDF
Helmut Prodinger
Abstract: A variation of Dyck paths allows for down-steps of arbitrary length, not just one. Credits for this invention are given to Emeric Deutsch. Surprisingly, the enumeration of them is somewhat akin to the analysis of Motzkin-paths; the last section contains a bijection.
Certain new subclasses of \(m\)-fold symmetric bi-pseudo-starlike functions using \(Q\)-derivative operator
OMA-Vol. 5 (2021), Issue 1, pp. 42 – 50 Open Access Full-Text PDF
Timilehin Gideon Shaba
Abstract: In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.
Fixed point theorems for generalized \(\left( \psi ,\varphi ,F\right)\)-contraction type mappings in \(b\)-metric spaces with Applications
OMA-Vol. 5 (2021), Issue 1, pp. 35 – 41 Open Access Full-Text PDF
Taieb Hamaizia
Abstract: The purpose of this paper is to prove a fixed point theorem for \(C\)-class functions in complete \(b\)-metric spaces. Moreover, the solution of the integral equation is obtained using our main result.
A new forms of extended hypergeometric functions and their properties
EASL-Vol. 4 (2021), Issue 1, pp. 30 – 41 Open Access Full-Text PDF
Ahmed Ali Al-Gonah, Waleed Khadher Mohammed
Abstract: In this paper, a new forms of extended hypergeometric functions are introduced. Some functional relations, integral representations and transformation formulas for these functions are derived.
Study of inequalities for unified integral operators of generalized convex functions
OMS-Vol. 5 (2021), Issue 1, pp. 80 – 93 Open Access Full-Text PDF
G. Farid, K. Mahreen, Yu-Ming Chu
Abstract: The aim of this paper is to study unified integral operators for generalized convex functions namely \((\alpha,h-m)\)-convex functions. We obtained upper as well as lower bounds of these integral operators in diverse forms. The results simultaneously hold for many kinds of well known fractional integral operators and for various kinds of convex functions.
Strong quasi-ordered residuated system
OMS-Vol. 5 (2021), Issue 1, pp. 73 – 79 Open Access Full-Text PDF
Daniel A. Romano
Abstract: The concept of residuated relational systems ordered under a quasi-order relation was introduced in 2018 by S. Bonzio and I. Chajda. In such algebraic systems, we have introduced and developed the concepts of implicative and comparative filters. In addition, we have shown that every comparative filter is an implicative filter at the same time and that converse it does not have to be. In this article, as a continuation of previous research, we introduce the concept of strong quasi-ordered residuated systems and we show that in such systems implicative and comparative filters coincide. In addition, we show that in such systems the concept of least upper bound for any two pair of elements can be determined.
Inequalities approach in determination of convergence of recurrence sequences
OMS-Vol. 5 (2021), Issue 1, pp. 65 – 72 Open Access Full-Text PDF
Albert Adu-Sackey, Francis T. Oduro, Gabriel Obed Fosu
Abstract: The paper proves convergence for three uniquely defined recursive sequences, namely, arithmetico-geometric sequence, the Newton-Raphson recursive sequence, and the nested/composite recursive sequence. The three main hurdles for this prove processes are boundedness, monotonicity, and convergence. Oftentimes, these processes lie in the predominant use of prove by mathematical induction and also require some bit of creativity and inspiration drawn from the convergence monotone theorem. However, these techniques are not adopted here, rather, as a novelty, extensive use of basic manipulation of inequalities and useful equations are applied in illustrating convergence for these sequences. Moreover, we established a mathematical expression for the limit of the nested recurrence sequence in terms of its leading term which yields favorable results.
Generalized orthopair fuzzy sets based on Hamacher T-norm and T-conorm
OMS-Vol. 5 (2021), Issue 1, pp. 44 – 64 Open Access Full-Text PDF
I. Silambarasan
Abstract: The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the \(q^{th}\) power of the truth-membership and the \(q^{th}\) power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter \(q, ~q\geq 1\). In this paper, we define the Hamacher operations of q-rung orthopair fuzzy sets and proved some desirable properties of these operations, such as commutativity, idempotency, and monotonicity. Further, we proved De Morgan’s laws for these operations over complement. Furthermore, we defined the Hamacher scalar multiplication \(({n._{h}}A)\) and Hamacher exponentiation \((A^{\wedge_{h}n})\) operations on q-rung orthopair fuzzy sets and investigated their algebraic properties. Finally, we defined the necessity and possibility operators based on q-rung orthopair fuzzy sets and some properties of Hamacher operations that are considered.