A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
3
4
2021
12
01
An existence result for a class of (p(x),q(x))-Laplacian system via sub-supersolution method
1
8
EN
Saleh
Shakeri
Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, P. O. Box 678, Iran
s.shakeri@umz.ac.ir
10.30495/maca.2021.1937515.1024
This study concerns the existence of positive solution for the following nonlinear boundary value problem<br />begin{gather*}<br />-Delta_{p(x)} u= a(x)h(u) + f(v) quadtext{in }Omega\<br />-Delta_{q(x)} v=b(x)k(v) + g(u) quadtext{in }Omega\<br />u=v= 0 quadtext{on } partial Omega<br />end{gather*}<br />where $p(x),q(x) in C^1(mathbb{R}^N)$ are radial symmetric functions such that $sup|nabla p(x)| < infty,$ $sup|nabla q(x)|<infty$ and $1 < inf p(x) leq sup p(x) <infty,1 < inf q(x) leq sup q(x) < infty$, and where $-Delta_{p(x)} u = -mathop{rm div}|nabla u|^{p(x)-2}nabla u,-Delta_{q(x)} v =-mathop{rm div}|nabla v|^{q(x)-2}nabla v$ respectively are called $p(x)$-Laplacian and $q(x)$-Laplacian, $Omega = B(0 , R) = {x | |x| < R}$ is a bounded radial symmetric domain, where $R > 0$ is a sufficiently large constant. We discuss the existence of positive solution via sub-supersolutions without assuming sign conditions on $f(0)$ and $g(0)$.
Positive radial solutions,(p(x),q(x))-Laplacian system,Sub-super solutions
http://www.macajournal.com/article_685401.html
http://www.macajournal.com/article_685401_bf81051cb14c0238acbe5412b52fd812.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
3
4
2021
12
01
On closedness of convolution of two sets
9
12
EN
Seyyed Mohammad
Tabatabaie
Department of Mathematics, University of Qom, Qom, Iran
sm.tabatabaie@qom.ac.ir
10.30495/maca.2021.1935853.1020
In this note, we give an abstract version of the fact that convolution of two closed and compact subsets of a hypergroup is a closed set.
locally compact group,locally compact hypergroup,Michael topology
http://www.macajournal.com/article_685578.html
http://www.macajournal.com/article_685578_0667a5097e65cd0dc09860c42fe2a77f.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
3
4
2021
12
01
On a nonlinear abstract second-order integrodifferential equation part I
13
24
EN
Mohammed
Aijazuddin
Hussain
0000-0003-4204-0679
H.no 3-8-44\slash2(1-25-176), Manzoorpura, Near Shahgunj, Aurangabad (431001), Maharashtra, India
aijazuddinhussain044@gmail.com
10.30495/maca.2021.1936023.1022
The object of this paper is to study the existence, uniqueness and continuation of the solutions of nonlinear second-order integrodifferential equations. In the theory of infinitesimal generator of $C_0$- semigroup in a Banach space, the fixed point theorems of Schauder and Banach are used to establish our main results.
Integrodifferential equation,Kernal,Fixed point theorem,C0-semigroup theory
http://www.macajournal.com/article_685579.html
http://www.macajournal.com/article_685579_252fa30ee6eae90f5a07fdad068b1c66.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
3
4
2021
12
01
Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials
25
40
EN
Mohammad Hossein
Derakhshan
Department of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, Iran
m.h.derakhshan.20@gmail.com
10.30495/maca.2021.1938222.1025
In this paper, an efficient numerical method based on operational matrices of the second kind Chebyshev polynomials is used for the solution of a coupled system of fractional-order integrodifferential equations that the fractional derivative is given in Caputo's sense. The operational matrices of the second kind Chebyshev polynomials reduce the given equations to a system of linear algebraic equations. An approximate solution is calculated by extending the functions in terms of the second kind Chebyshev polynomials and applying operational matrices. Unknown coefficients are obtained by solving the final system of linear equations. Also, convergence analysis and error bound of the solution are studied in this paper. Moreover, to check the reliability and accuracy of the given method. The numerical examples have been shown and the results of the described method are compared with the Haar wavelet method. The obtained results authenticate that the displayed method is effortless to analyze and perform such types of problems. All methods for the proposed method are applied in MATLAB (R2020b) software.
Integro differential equations,Operational matrix,Second kind Chebyshev polynomials,Numerical solutions
http://www.macajournal.com/article_685644.html
http://www.macajournal.com/article_685644_23f14b286fa615fb690c448b625b9a9b.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
3
4
2021
12
01
Multiplicity results for the nonlinear p-Laplacian fractional boundary value problems
41
62
EN
Tawanda Gallan
Chakuvinga
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey
tchakuvinga@gmail.com
Fatma Serap
Topal
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey
f.serap.topal@ege.edu.tr
10.30495/maca.2021.1938349.1026
This paper investigates the existence of single and multiple positive positive solutions of fractional differential equations with p-Laplacian by means of the Green's function properties, the Guo-Krasnosel'skii fixed point theorem, the monotone iterative technique accompanied by established sufficient conditions and the Leggett-Williams fixed point theorem. Additionally, the main results are illustrated by some examples to show their validity.
Riemann-Liouville fractional derivative,p-Laplacian operator,Fixed point theorems,Boundary value problems
http://www.macajournal.com/article_686168.html
http://www.macajournal.com/article_686168_4d65d67d764c3138e2e501d1fba96748.pdf
A.I.A University Publishing Group.
Mathematical Analysis and its Contemporary Applications
2716-9890
2716-9898
3
4
2021
12
01
Bifuzzy d-algebras under norms
63
83
EN
Rasul
Rasuli
Department of Mathematics, Payame Noor University, Tehran, Iran.
rasulirasul@yahoo.com
10.30495/maca.2021.1938454.1027
In this paper, by using norms (t-norms and t-conorms), we introduce the notions of bifuzzy d-algebras and bifuzzy d-ideals of d-algebras and investigate several interesting properties. Next, we consider their intersection and product. Finally, we obtain some results about them under d-algebra homomorphisms.
Algebra and orders,theory of fuzzy sets,bifuzzy sets,Norms,products and intersections,homomorphisms
http://www.macajournal.com/article_685803.html
http://www.macajournal.com/article_685803_34880c5e15307e9ddc2ffe920f7829e7.pdf