ORIGINAL_ARTICLE
An existence result for a class of (p(x),q(x))-Laplacian system via sub-supersolution method
This study concerns the existence of positive solution for the following nonlinear boundary value problem\begin{gather*}-\Delta_{p(x)} u= a(x)h(u) + f(v) \quad\text{in }\Omega\\-\Delta_{q(x)} v=b(x)k(v) + g(u) \quad\text{in }\Omega\\u=v= 0 \quad\text{on } \partial \Omega\end{gather*}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 $g(0)$.
http://www.macajournal.com/article_685401_bf81051cb14c0238acbe5412b52fd812.pdf
2021-12-01
1
8
10.30495/maca.2021.1937515.1024
Positive radial solutions
(p(x),q(x))-Laplacian system
Sub-super solutions
Saleh
Shakeri
s.shakeri@umz.ac.ir
1
Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, P. O. Box 678, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
On closedness of convolution of two sets
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.
http://www.macajournal.com/article_685578_0667a5097e65cd0dc09860c42fe2a77f.pdf
2021-12-01
9
12
10.30495/maca.2021.1935853.1020
locally compact group
locally compact hypergroup
Michael topology
Seyyed Mohammad
Tabatabaie
sm.tabatabaie@qom.ac.ir
1
Department of Mathematics, University of Qom, Qom, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
On a nonlinear abstract second-order integrodifferential equation part I
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.
http://www.macajournal.com/article_685579_252fa30ee6eae90f5a07fdad068b1c66.pdf
2021-12-01
13
24
10.30495/maca.2021.1936023.1022
Integrodifferential equation
Kernal
Fixed point theorem
C0-semigroup theory
Mohammed
Hussain
aijazuddinhussain044@gmail.com
1
H.no 3-8-44\slash2(1-25-176), Manzoorpura, Near Shahgunj, Aurangabad (431001), Maharashtra, India
LEAD_AUTHOR
ORIGINAL_ARTICLE
Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials
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.
http://www.macajournal.com/article_685644_23f14b286fa615fb690c448b625b9a9b.pdf
2021-12-01
25
40
10.30495/maca.2021.1938222.1025
Integro differential equations
Operational matrix
Second kind Chebyshev polynomials
Numerical solutions
Mohammad Hossein
Derakhshan
m.h.derakhshan.20@gmail.com
1
Department of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Multiplicity results for the nonlinear p-Laplacian fractional boundary value problems
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.
http://www.macajournal.com/article_686168_4d65d67d764c3138e2e501d1fba96748.pdf
2021-12-01
41
62
10.30495/maca.2021.1938349.1026
Riemann-Liouville fractional derivative
p-Laplacian operator
Fixed point theorems
Boundary value problems
Tawanda Gallan
Chakuvinga
tchakuvinga@gmail.com
1
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey
AUTHOR
Fatma Serap
Topal
f.serap.topal@ege.edu.tr
2
Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey
LEAD_AUTHOR
ORIGINAL_ARTICLE
Bifuzzy d-algebras under norms
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.
http://www.macajournal.com/article_685803_34880c5e15307e9ddc2ffe920f7829e7.pdf
2021-12-01
63
83
10.30495/maca.2021.1938454.1027
Algebra and orders
theory of fuzzy sets
bifuzzy sets
Norms
products and intersections
homomorphisms
Rasul
Rasuli
rasulirasul@yahoo.com
1
Department of Mathematics, Payame Noor University, Tehran, Iran.
LEAD_AUTHOR