]>
2023
28
2
89
Exact solution for commensurate and incommensurate linear systems of fractional differential equations
Exact solution for commensurate and incommensurate linear systems of fractional differential equations
en
en
In this paper, we introduce exact solutions for the initial value problems of two classes of a linear system of fractional ordinary differential equations with constant coefficients. This article concerns a linear system of fractional order, where the orders are equal or different rational numbers between zero and one. The conformable fractional derivative presented by [R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, J. Comput. Appl. Math., \(\textbf{264}\) (2014), 65--70] is considered. Two different approaches are adopted to give analytic solutions for fractional order systems. The presented methods are illustrated by analyzing some numerical examples that show the effectiveness of the implemented methods.
123
136
A.
Al-Habahbeh
Department of Mathematics
Tafila Technical University
Jordan
aaalhaba@ttu.edu.jo
Conformable fractional derivative
fractional Laplace transform
commensurate and incommensurate fractional order systems
asymptotically stable
Article.1.pdf
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[1]
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57-66
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M. Abu Hammad, R. Khalil, Abel’s Formula and Wronskian for Conformable Fractional Differential Equations, Int. J. Differ. Equ. Appl., 13 (2014), 1-11
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I. Abu Hammad, R. Khalil, Fractional fourier series with applications, Amer. J. Comput. Appl. Math., 4 (2014), 187-191
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A. Akbulut, M. Kaplan, Auxiliary equation method for time-fractional differential equations with conformable derivative, Comput. Math. Appl., 75 (2018), 876-882
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M. Al-Horani, R. Khalil, I. Aldarawi, Fractional Cauchy Euler Differential Equation, J. Comput. Anal. Appl., 28 (2020), 1-13
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M. Alsauodi, M. Alhorani, R. Khalil, Solutions of Certain Fractional Partial Differential Equations, WSEAS Trans. Math., 20 (2021), 504-507
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D. R. Anderson, E. Camrud, D. J. Ulness, On the nature of the conformable derivative and its applications to physics, J. Fract. Calc. Appl., 10 (2019), 92-135
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D. Baleanu, H. Mohammadi, S. Rezapour, A mathematical theoretical study of a particular system of Caputo–Fabrizio fractional differential equations for the Rubella disease model, Adv. Difference Equ., 2020 (2020), 1-19
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I. Benkemache, M. Al-Horani, R. Khalil, Tensor Product and Certain Solutions of Fractional Wave Type Equation, Eur. J. Pure Appl. Math., 14 (2021), 942-948
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S. Buedo-Fernandez, J. J. Nieto, Basic control theory for linear fractional differential equations with constant coefficients, Frontiers in Phys., 8 (2020), 1-12
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L. Debnath, Recent applications of fractional calculus to science and engineering, Int. J. Math. Math. Sci., 2003 (2003), 3413-3442
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K. Diethelm, N. J. Ford, Analysis of freactional differential equations, J. Math. Anal. Appl., 265 (2002), 229-248
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K. Diethelm, N. J. Ford, A. D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynam., 29 (2002), 3-22
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]
Existence and uniqueness results of mild solutions for integro-differential Volterra-Fredholm equations
Existence and uniqueness results of mild solutions for integro-differential Volterra-Fredholm equations
en
en
In this paper, we demonstrate the existence and uniqueness of mild and classical solutions to an integro-differential non-local Volterra-Fredholm quasilinear delay.
The findings are derived by applying the fixed point theorems of $\Re_0$-Semigroup and the Banach.
137
144
K. H.
Hussain
Department of Mechanical Technology, Basra Technical Institute
Southern Technical University
Iraq
khawlah.hussain@stu.edu.iq
Volterra-Fredholm integro-differential equation
nonlocal condition
Banach fixed point theorem
Article.2.pdf
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Caputo fractional order derivative model of Zika virus transmission dynamics
Caputo fractional order derivative model of Zika virus transmission dynamics
en
en
The Zika Virus (ZIKV) is a highly contagious disease, and several outbreaks have occurred since it emerged. It is transmitted from one to another human via a mosquito Aedes aegypti. There is no vaccine or established medicine available for ZIKV to date. There is an urgent need to enhance an understanding of the progression mechanism of the disease when drugs or vaccines are not available. Mathematical modeling is a tool that might be helpful to understand the progression dynamics of ZIKV which can enable us to make control strategies for invading the progression dynamics of disease. SEIR-SEI is a famous compartmental deterministic modeling based on integer-order derivative calculus. Nowadays, conversion from integer to fractional order-based derivative modeling is in trend, and it is a very effective and high degree of accuracy. In this paper, we proposed a Caputo fractional-order based susceptible-exposed-infected-recovered (SEIR) structure for hosts and a susceptible-exposed-infected (SEI) structure for mosquitoes for transmission dynamics of ZIKV. For this purpose, we modified the classical compartmental model used in the study of progression dynamics of the Zika fever outbreak in El-Salvador during 2015-16. The modified model involves nonlinear differential equations of fractional (non-integer) order which has an advantage over the classical model due to its memory effect property. Our study includes eight regions across the globe where the Zika outbreak has occurred during the year 2013-2016 including six major archipelagos of French Polynesia, i.e., Tahiti, Sous-le-vent, Moorea, Tuamotu, Marquises, and Australes. The other two regions included Costa Rica and Colombia. The outbreak in selected regions was studied first using a classical model and then compared by a fractional-order model. The data of outbreaks are best fitted with the fractional-order model which enables us to estimate the best parameters values for the outbreaks. Using this modeling, the epidemic threshold parameter $R_0$ was computed which is more accurate than the classical one. Hence, the fractional-order model for ZIKV transmission dynamics is much better prediction, analysis, and disease parameters estimation than the classical model. This modeling enhances the knowledge in the field of fractional order and understanding the ZIKV transmission accurately.
145
157
R.
Prasad
Department of Mathematics
Gargi College (University of Delhi)
India
ramakant.prasad@gargi.du.ac.in
K.
Kumar
Department of Mathematics
Atma Ram Sanatan Dharma College (University of Delhi)
India
kapilkumarmaths@gmail.com
R.
Dohare
Centre for Interdisciplinary Research in Basic Sciences
Jamia Millia Islamia
India
ravinsdohare@gmail.com
Fractional-order
transmission dynamics
basics reproduction number
ZIKV
Article.3.pdf
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]
\((3, 4)\)-fuzzy sets and their topological spaces
\((3, 4)\)-fuzzy sets and their topological spaces
en
en
The aim of this paper is to introduce the concept of \((3, 4)\)-fuzzy sets. We compare \((3, 4)\)-fuzzy sets with intuitionistic fuzzy sets, Pythagorean fuzzy sets, and Fermatean fuzzy sets. We focus on the complement of \((3, 4)\)-fuzzy sets. We construct some of the fundamental set of operations of the \((3, 4)\)-fuzzy sets. Due to their larger range of describing membership grades, \((3, 4)\)-fuzzy sets can deal with more uncertain situations than other types of fuzzy sets. For ranking \((3, 4)\)-fuzzy sets, we define a score function and an accuracy function. In addition, we introduce the concept of \((3, 4)\)-fuzzy topological space. Ultimately, we define \((3, 4)\)-fuzzy continuity of a map defined between \((3, 4)\)-fuzzy topological spaces and we characterize this concept.
158
170
Kh. Kh.
Murad
Department of Mathematics, Faculty of Science
University of Zakho
Iraq
H. Z.
Ibrahim
Department of Mathematics, Faculty of Education
University of Zakho
Iraq
hariwan_math@yahoo.com
\((3, 4)\)-fuzzy sets
operations
\((3, 4)\)-fuzzy topology
\((3, 4)\)-fuzzy continuous
Article.4.pdf
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]
CR-fuzzy sets and their applications
CR-fuzzy sets and their applications
en
en
Pythagorean fuzzy set is one of the successful extensions of the fuzzy set for handling uncertainties in information. Under this environment, in this paper, we introduce a new type of generalized fuzzy sets is called CR-fuzzy sets and compare CR-fuzzy sets with Pythagorean fuzzy sets and Fermatean fuzzy sets. The set operations, score function and accuracy function of CR-fuzzy sets will study along with their several properties.
171
181
Y. A.
Salih
Department of Mathematics, College of Science
University of Duhok
Iraq
H. Z.
Ibrahim
Department of Mathematics, Faculty of Education
University of Zakho
Iraq
hariwan_math@yahoo.com
CR-fuzzy sets
operations
score function
accuracy function
Article.5.pdf
[
[1]
B. Ahmad, A. Kharal, On fuzzy soft sets, Adv. Fuzzy Syst., 2009 (2009), 1-6
##[2]
T. M. Al-shami, H. Z. Ibrahim, A. A. Azzam, A. I. EL-Maghrabi, SR-Fuzzy sets and their weighted aggregated operators in applications to decision-making, J. Funct. Spaces, 2022 (2022), 1-14
##[3]
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96
##[4]
M. Atef, M. I. Ali, T. M. Al-shami, Fuzzy soft covering based multi-granulation fuzzy rough sets and their applications, Comput. Appl. Math., 40 (2021), 1-26
##[5]
N. Cagman, S. Enginoglu, F. Citak, Fuzzy soft set theory and its application, Iran. J. Fuzzy Syst., 8 (2011), 137-147
##[6]
H. Garg, Anewimproved score function of an interval-valued Pythagorean fuzzy set based TOPSIS method, Int. J. Uncertain. Quantif., 7 (20147), 463-474
##[7]
H. Garg, K. Kumar, An advance study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft. Comput., 22 (2018), 4959-4970
##[8]
H. Garg, K. Kumar, Distance measures for connection number sets based on set pair analysis and its applications to decision making process, Appl. Intel., 48 (2018), 3346-3359
##[9]
H. Garg, S. Singh, A novel triangular interval type-2 intuitionistic fuzzy set and their aggregation operators, Iran. J. Fuzzy Syst., 15 (2018), 69-93
##[10]
H. Z. Ibrahim, T. M. Al-shami, O. G. Elbarbary, (3, 2)-fuzzy sets and their applications to topology and optimal choice, Computational Intelligence and Neuroscience, 2021 (2021), 1-14
##[11]
H. J. Ko, Stability Analysis of Digital Filters Under Finite Word Length Effects via Normal-Form Transformation, Asian J. Health Infor. Sci., 1 (2006), 112-121
##[12]
T. Senapati, R. R. Yager, Some new operations over fermatean fuzzy numbers and application of fermatean fuzzy WPM in multiple criteria decision making, Informatica, 30 (2019), 391-412
##[13]
T. Senapati, R. R. Yager, Fermatean fuzzy sets, Journal of Ambient Intelligence and Humanized Computing, 11 (2020), 663-674
##[14]
R. R. Yager, Pythagorean fuzzy subsets, Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting (Edmonton, Canada),, 2013 (2013), 57-61
##[15]
L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338-353
]
Ideal theory of semigroups based on \((3,2)\)-fuzzy sets
Ideal theory of semigroups based on \((3,2)\)-fuzzy sets
en
en
In this paper, the notions of \((3,2)\)-fuzzy ideal, \((3,2)\)-fuzzy bi-ideal, \((3,2)\)-fuzzy interior ideal and \((3,2)\)-fuzzy \((1,2)\)-ideal of a semigroup are introduced and investigated their properties. The relation between (\((3,2)\)-fuzzy) ideal, bi-ideal, interior ideal and \((1,2)\)-ideal are given. We characterized \((3,2)\)-fuzzy \((1,2)\)-ideal in terms of \(f^3\)-level \(\alpha\)-cut and \(g^2\)-level \(\alpha\)-cut. A necessary and sufficient condition for a subset of a semigroup to be \((1,2)\)-ideal in terms of \((3,2)\)-fuzzy \((1,2)\)-ideal of a semigroup is given.
182
191
M.
Vanishree
Department of Mathematics
Rajah Serfoji Government College (affliated to Bharathidasan University)
India
tmrvani@gmail.com
N.
Rajesh
Department of Mathematics
Rajah Serfoji Government College
India
nrajesh_topology@yahoo.co.in
N.
Rafi
Department of Mathematics
Bapatla Engineering College
India
rafimaths@gmail.com
R.
Bandaru
Department of Mathematics
GITAM (Deemed to be University)
India
ravimaths83@gmail.com
\((3,2)\)-fuzzy set
\((3,2)\)-fuzzy subalgebra
\((3,2)\)-fuzzy ideal
Article.6.pdf
[
[1]
B. Ahmad, A. Kharal, On fuzzy soft sets,, Adv. Fuzzy Syst., 2009 (2009), 1-6
##[2]
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96
##[3]
M. Atef, M. I. Ali, T. M. Al-shami, Fuzzy soft covering based multi-granulation fuzzy rough sets and their applications, Comput. Appl. Math., 40 (2021), 1-26
##[4]
N. Cagman, S. Enginoglu, F. Citak, Fuzzy soft set theory and its application, Iran. J. Fuzzy Syst., 8 (2011), 137-147
##[5]
H. Garg, S. Singh, A novel triangular interval type-2 intuitionistic fuzzy set and their aggregation operators, Iran. J. Fuzzy Syst., 15 (2018), 69-93
##[6]
H. Garg, K. Kumar, An advance study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft. Comput.,, 22 (2018), 4959-4970
##[7]
H. Garg, K. Kumar, Distance measures for connection number sets based on set pair analysis and its applications to decision making process, Appl. Intel., 48 (2018), 3346-3359
##[8]
H. Z. Ibrahim, T. M. Al-shami, O. G. Elbarbary, (3, 2)-fuzzy sets and their applications to topology and optimal choice, Computational Intelligence and Neuroscience,, 2021 (2021), 1-14
##[9]
K. H. Kim, Y. B. Jun, Intuitionistic fuzzy ideals of semigroups, Indian J. Pure Appl. Math.,, 33 (2002), 443-449
##[10]
T. Senapati, R. R. Yager, Fermatean fuzzy sets, Journal of Ambient Intelligence and Humanized Computing,, 11 (2020), 663-674
##[11]
R. R. Yager, Pythagorean fuzzy subsets, Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting (Edmonton, Canada),, 2013 (2013), 57-61
##[12]
L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338-353
]
New oscillation criteria and some refinements for second-order neutral delay dynamic equations on time scales
New oscillation criteria and some refinements for second-order neutral delay dynamic equations on time scales
en
en
In this paper, we present more effective criteria for oscillation of second-order half-linear neutral dynamic equations with delayed arguments. Our results essentially improve, complement,
and simplify several related ones in the literature. Some examples are given to illustrate our main
results.
192
202
A. M.
Hassan
Department of Mathematics, Faculty of Science
Benha University
Egypt
ahmed.mohamed@fsc.bu.edu.eg
S. E.
Affan
Department of Mathematics, Faculty of Science
Benha University
Egypt
samy.affan@fsc.bu.edu.eg
Second order
nonlinear dynamic equations
oscillation
Riccati transformation
Article.7.pdf
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M. Bohner, T. S. Hassan, T. X. Li, Fite-Hille-Wintner-type oscillation criteria for second-order half-linear dynamic equation with deviating arguments, Indag. Math. (N.S.), 29 (2018), 548-560
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G. E. Chatzarakis, I. Jadlovska, Improved oscillation results for second-order half-linear delay differential equations, Hacet. J. Math. Stat., 48 (2019), 170-179
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G. Viglialoro, T. E. Woolley, Boundedness in a parabolic-elliptic chemotaxis system with nonlinear diffusion and sensitivity and logistic source, Math. Methods Appl. Sci., 41 (2018), 1809-1824
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]
A computational method on derivative variations of optimal control
A computational method on derivative variations of optimal control
en
en
In this paper, we propose an algorithm for solving optimal control problems
in a class of continuously differentiable control functions with bounded derivatives. Based on
derivative variations [R. Enkhbat, B. Barsbold,
J. Mongolian Math. Soc., \(\bf 17\) (2013), 27--39], we derive new optimality conditions for the original problem.
An algorithm has been constructed based on the optimality conditions. The convergence of the proposed
algorithm has been proved. The algorithm was tested on some well known numerical examples.
203
212
E.
Rentsen
The Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences
National University of Mongolia
Mongolia
M.
Kamada
Department of Computer and Information Sciences
Ibaraki University
Japan
A.
Radwan
Department of Mathematics, College of Science
Department of Mathematics, Faculty of Science
Jouf University
Sohag University
Kingdom of Saudi Arabia
Egypt
amaradwan@ju.edu.sa
W.
Alrashdan
Department of Mathematics, College of Science
Jouf University
Kingdom of Saudi Arabia
Calculus of variations
optimal control
derivative variation
optimality conditions
Article.8.pdf
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]