Maca Islamic Azad university Ardabil Mathematical Analysis and its Contemporary Applications 2716-9890 Islamic Azad university Ardabil 685401 10.30495/maca.2021.1937515.1024 Original Article An existence result for a class of (p(x),q(x))-Laplacian system via sub-supersolution method An existence result for a class of (p(x),q(x))-Laplacian system via sub-supersolution method Shakeri Saleh Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, P. O. Box 678, Iran 01 12 2021 3 4 1 8 10 08 2021 23 09 2021 Copyright © 2021, Islamic Azad university Ardabil. 2021 http://www.macajournal.com/article_685401.html

This study concerns the existence of positive solution for the following nonlinear boundary value problembegin{gather*}-Delta_{p(x)} u= a(x)h(u) + f(v) quadtext{in }Omega\-Delta_{q(x)} v=b(x)k(v) + g(u) quadtext{in }Omega\u=v= 0 quadtext{on } partial Omegaend{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)\$.

Positive radial solutions (p(x),q(x))-Laplacian system Sub-super solutions
Maca Islamic Azad university Ardabil Mathematical Analysis and its Contemporary Applications 2716-9890 Islamic Azad university Ardabil 685578 10.30495/maca.2021.1935853.1020 Original Article On closedness of convolution of two sets On closedness of convolution of two sets Tabatabaie Seyyed Mohammad Department of Mathematics, University of Qom, Qom, Iran 01 12 2021 3 4 9 12 18 07 2021 26 09 2021 Copyright © 2021, Islamic Azad university Ardabil. 2021 http://www.macajournal.com/article_685578.html

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
Maca Islamic Azad university Ardabil Mathematical Analysis and its Contemporary Applications 2716-9890 Islamic Azad university Ardabil 685579 10.30495/maca.2021.1936023.1022 Original Article On a nonlinear abstract second-order integrodifferential equation part I On a nonlinear abstract second order integro differential equation part I Hussain Mohammed Aijazuddin H.no 3-8-44\slash2(1-25-176), Manzoorpura, Near Shahgunj, Aurangabad (431001), Maharashtra, India 01 12 2021 3 4 13 24 19 07 2021 28 09 2021 Copyright © 2021, Islamic Azad university Ardabil. 2021 http://www.macajournal.com/article_685579.html

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
Maca Islamic Azad university Ardabil Mathematical Analysis and its Contemporary Applications 2716-9890 Islamic Azad university Ardabil 685644 10.30495/maca.2021.1938222.1025 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 Numerical solution of a coupled system of fractional order integro differential equations by an efficient numerical method based on the second kind Chebyshev polynomials Derakhshan Mohammad Hossein Department of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, Iran 01 12 2021 3 4 25 40 19 08 2021 09 10 2021 Copyright © 2021, Islamic Azad university Ardabil. 2021 http://www.macajournal.com/article_685644.html

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
Maca Islamic Azad university Ardabil Mathematical Analysis and its Contemporary Applications 2716-9890 Islamic Azad university Ardabil 686168 10.30495/maca.2021.1938349.1026 Original Article Multiplicity results for the nonlinear p-Laplacian fractional boundary value problems p-Laplacian fractional boundary value problems Chakuvinga Tawanda Gallan Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey Topal Fatma Serap Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey 01 12 2021 3 4 41 62 21 08 2021 04 11 2021 Copyright © 2021, Islamic Azad university Ardabil. 2021 http://www.macajournal.com/article_686168.html

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
Maca Islamic Azad university Ardabil Mathematical Analysis and its Contemporary Applications 2716-9890 Islamic Azad university Ardabil 685803 10.30495/maca.2021.1938454.1027 Original Article Bifuzzy d-algebras under norms Bifuzzy d-algebras under norms Rasuli Rasul Department of Mathematics, Payame Noor University, Tehran, Iran. 01 12 2021 3 4 63 83 22 08 2021 17 10 2021 Copyright © 2021, Islamic Azad university Ardabil. 2021 http://www.macajournal.com/article_685803.html

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