A foundation on semigroups of operators defined on the set of triangular fuzzy numbers and its application to fuzzy fractional evolution equations

2018 ◽  
Vol 347 ◽  
pp. 1-28 ◽  
Author(s):  
Nguyen Thi Kim Son
2021 ◽  
Vol 24 (6) ◽  
pp. 1758-1776
Author(s):  
Xuping Zhang ◽  
Pengyu Chen ◽  
Donal O’Regan

Abstract In this article, we are concerned with the VIP of fractional fuzzy evolution equations in the space of triangular fuzzy numbers. The continuous dependence of two kinds of fuzzy mild solutions on initial values and orders for the studied problem is obtained. The results obtained in this paper improve and extend some related conclusions on this topic.


2018 ◽  
Vol 9 (11) ◽  
pp. 1717-1727
Author(s):  
Ajay Minj ◽  
Pathinathan T.

2021 ◽  
Vol 11 (8) ◽  
pp. 3555
Author(s):  
Chien-Hsiung Chen ◽  
Zhongzhen Lin

In the present era, technology is developing rapidly. Smartphones play a significant part in people’s lives. However, the research on smartphones mainly focuses on the area of technological realization. The purposes of this study were to examine the relationship between the various rear cameras in smartphones and consumer perceptions, and to understand consumers’ purchasing intentions and preferences. Through the methods of multidimensional scaling (MDS), factor analysis and triangular fuzzy numbers, the visual images of the smartphone rear cameras were analyzed and discussed. The results indicate that the visual images taken by different shapes of rear camera are quite distinct in the categories of innovative and fashionable, and simple and pure, but less distinct in the categories of harmonious and ordered, premium and technical, and superior and valuable. Through a comprehensive comparison, four groups whose images were similar were created. The outcome effectively reflects the potential consumer demands for smartphone rear camera patterns, providing insights for design practices in the smartphone industry.


2020 ◽  
Vol 23 (6) ◽  
pp. 1663-1677
Author(s):  
Michael Ruzhansky ◽  
Berikbol T. Torebek

Abstract The paper is devoted to study multidimensional van der Corput-type estimates for the intergrals involving Mittag-Leffler functions. The generalisation is that we replace the exponential function with the Mittag-Leffler-type function, to study multidimensional oscillatory integrals appearing in the analysis of time-fractional evolution equations. More specifically, we study two types of integrals with functions E α, β (i λ ϕ(x)), x ∈ ℝ N and E α, β (i α λ ϕ(x)), x ∈ ℝ N for the various range of α and β. Several generalisations of the van der Corput-type estimates are proved. As an application of the above results, the Cauchy problem for the multidimensional time-fractional Klein-Gordon and time-fractional Schrödinger equations are considered.


2021 ◽  
Vol 60 (4) ◽  
pp. 3741-3749
Author(s):  
Pallavi Bedi ◽  
Anoop Kumar ◽  
Thabet Abdeljawad ◽  
Aziz Khan

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li

AbstractIn this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the $(\alpha ,\beta )$ ( α , β ) -resolvent operator, we concern with the term $u'(\cdot )$ u ′ ( ⋅ ) and finding a control v such that the mild solution satisfies $u(b)=u_{b}$ u ( b ) = u b and $u'(b)=u'_{b}$ u ′ ( b ) = u b ′ . Finally, we present an application to support the validity study.


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