Book ChapterDOI
Local Fractional Calculus to Design the Growth System of Covid-19 Using Measure of Non-compactness
Hemant Kumar Nashine,Rabha W. Ibrahim +1 more
- pp 447-463
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In this paper, the authors used the concept of local fractional calculus and measure of noncompactness to design the growth system of Covid-19, and established a fixed point and coupled fixed point theorems for new set contraction condition in partially ordered Banach spaces, whose positive cone is normal.Abstract:
In this chapter, we use the concept of local fractional calculus and measure of non-compactness to design the growth system of Covid-19. To achieve this, we establish a fixed point and coupled fixed point theorems for new \(\mu \)-set contraction condition in partially ordered Banach spaces, whose positive cone \(\mathbb {K}\) is normal. We provide adequate examples to validate the epidemic dynamics with graphical presentations. We also use present available data to validate it.read more
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Proceedings ArticleDOI
K-symbol Fractional Complex Transform on Some Cantor Domains
Samir Hadid,Rabha W. Ibrahim +1 more
TL;DR: In this article , the k-symbol fractional complex transform (FSCT) was used for heat and Laplace operators on cantor domains, where local fractional differential operators (LFDOs) were used to manage differential equations.
References
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Journal ArticleDOI
A fixed point theorem in partially ordered sets and some applications to matrix equations
TL;DR: In this paper, an analogue of Banach's fixed point theorem in partially ordered sets is proved, and several applications to linear and nonlinear matrix equations are discussed, including the application of the Banach theorem to the Partially ordered Set (POPS) problem.
Journal ArticleDOI
Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations
TL;DR: It is proved the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a lower solution.
Journal ArticleDOI
Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations
TL;DR: In this article, the Banach contractive mapping theorem for partially ordered sets is extended to nonincreasing mappings as well as non-monotone mappings, and the existence of a unique solution admitting a lower solution is proved.