Mathematical Sciences and Applications
http://msa.wum.edu.pk/index.php/msa
<p>Mathematical Sciences and Applications is a comprehensive range of journals that publish original research and review articles on all fields of pure, applied, and computational mathematics. The journal focused on providing a platform for researchers to share their contributions across a wide range of disciplines, including but not limited to:</p> <p>Algebra, Number theory, Analysis, Topology Applied Analysis, Control Theory Discrete Mathematics, Fluid Dynamics, Mathematical Biology, Numerical Analysis, Probability Theory, Combinatorics, and Graph Theory.</p>The Women University Multanen-USMathematical Sciences and Applications2958-2903Reachability and Observability of Fractional Order Descriptor System
http://msa.wum.edu.pk/index.php/msa/article/view/15
<p>This work depends upon the state space models connected with generalized fractional order derivative with an additional multiple of matrix E (square and invertible matrix) in state vector x˙ (t)<sub>n×1</sub>. We have obtained the solution first and further the reachability and observability of this system using matrix conditions and KALMAN filter</p>Rimsha SeharDur-e-Sameen
Copyright (c) 2023 Mathematical Sciences and Applications
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2023-12-292023-12-292211810.52700/msa.v2i2.15Some Observability Conditions for a Fractional order Descriptor System; A new Approach
http://msa.wum.edu.pk/index.php/msa/article/view/13
<p>In this article, a descriptor systems involving singular and non-singular matrix $E_{n\times n}$ in the both input and output equation for the observability condition has been studied. The discussion is for both classical order derivative and Caputo's fractional order derivative.Firstly, the solution is obtained and further the observability conditions in form of Grammian matrices and rank conditions as per Kalman criteria are verified. These results are more generalized and can be verified for various special cases in the observability results for various types of descriptor systems.</p>Fatima Khan
Copyright (c) 2023 Fatima Khan
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2023-12-292023-12-2922193110.52700/msa.v2i2.13Fractional Derivatives with Applications: A Review
http://msa.wum.edu.pk/index.php/msa/article/view/17
<p>This paper presents a review of brief introduction to fractional calculus with the definitions of fractional derivatives and operators. Its properties and useful mathematical functions are specified. The fractional derivatives importance is seen in many fields and can be used in modeling various phenomena. The types of fractional derivatives are being added and focus is made on caputo derivatives with its usage in latest researches. Its merits and demerits are stated which give insight to understand caputo derivatives more effectively. This understanding will help generate and solve new problems arising in various fields such as mathematical physics, dynamical systems, fluid mechanics, statistics, biology, viscoelasticity and many more. The caputo derivative examples of some functions are listed in tabular form. The difference and comparison between two types of fractional derivatives namely, Riemann-Liouville and caputo derivatives are given. The highlighted portion is the latest research and problem solving made in different areas using caputo derivatives.</p>Fatima ShafiqMunazza Malik
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2023-12-312023-12-31223350Fuzzy Set Theory Applied on Li-Fraumeni Syndrome Homeopathic Selection of Remedies
http://msa.wum.edu.pk/index.php/msa/article/view/20
<p>In this study, by using the basic concepts and results of the Fuzzy Set Theory, the ambiguous circumstances of homeopathy, regarding the selection, dilution, and potencies are analyzed by parameterization concepts. A comprehensive study of Li-Fraumeni syndrome (LFS) as a genetic autosomal dominant disease is described as related to mutations in the P53 genes. The analysis of the effects and different potencies of some homeopathic medicines like Calcarea Fluorica, Thuja, Carcinosin, Phytolacca, and Calcarea Phos as complementary and alternative medicines are represented through the graphical representation of the different age groups of people. In the context of the Langmuir equation, the dilutions using the Hahnemann and Korsakovian methods with implementing the Fuzzy Set Theory are analyzed.</p>Rafia BashirMehwish Afzal
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2023-12-312023-12-3122517210.52700/msa.v2i2.20Unified Framework of Stationary and Non-Stationary Subdivision Schemes for Curve Modeling
http://msa.wum.edu.pk/index.php/msa/article/view/22
<p>In this study, we explore the interaction of two Laurent polynomials to generate a new polynomial through multiplication. Introducing a parameter allows us to adjust the number of factors within this polynomial, thereby facilitating the creation of a diverse family of non-stationary subdivision schemes. Each distinct value of the parameter corresponds to a unique member of this scheme family. Additionally, leveraging the concept of asymptotic equivalence, we derive a separate family of stationary schemes. Following the derivation of stationary schemes, we proceed to analyze their key characteristics and practical applications. This includes detailed examination of properties such as convergence behavior, polynomial generation degree, reproduction capabilities, continuity, and the structure of limit stencils. Furthermore, we explore the practical applications of these schemes in generating smooth curves.</p>Muhammad Adeel ShahzadRakib MustafaMuhammad AsgharGhulam Mustafa
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2023-12-312023-12-31227388