In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed.
Next, we review some basic concepts, notations, and technical results that are necessary in our study.
In Section 2, we state some basic concepts, notations and preliminary results about fractional calculus.
In Section 2, we state some basic concepts, notations and preliminary results about fractional calculus and measure of noncompactness.
First of all, let us recall some basic concepts, notations and known results which will be used in the sequel.
This article is organized as follows: In Section 2, we state some basic concepts, notations and properties about fractional order operator and measure of noncompactness.
The following section details the concept and notation of musical note, gamaka, and other symbols.
Throughout this paper, we denote (mathbb{R}^_{0} = [0, +infty)) and (mathbb{N}_{0} = mathbb{N} cup{0}), where (mathbb{N}) is the set of all positive integers. First, we recall some basic concepts and notation. The concept of b-metric was introduced by Czerwik [1] as a generalization of metric (see also Bakhtin [2, 3]) to extend the celebrated Banach contraction mapping principle.
No advanced know-how is required to understand this analysis; elementary set theory suffices (Cf. http://en.wikipedia.org/wiki/Set_theory – basic concepts and notation).
The Fourier transform of that periodic signal, defined as an impulse train, where the heights or areas of the impulses are proportional to the Fourier series coefficients, provides us with a mechanism for combining it together the concepts or notation of the Fourier series and Fourier transform.
