Solution of Nonlinear Fractional Differential Equations Using Adomain Decomposition Method
Issue:
Volume 6, Issue 4, December 2021
Pages:
111-119
Received:
19 September 2021
Accepted:
14 October 2021
Published:
28 October 2021
Abstract: In this paper, Adomian decomposition method (ADM) will apply to solve nonlinear fractional differential equations (FDEs) of Caputo sense. These type of equations is very important in engineering applications such as electrical networks, fluid flow, control theory and fractals theory. ADM give analytical solution in form of series solution so the convergence of the series solution and the error analysis will discuss. In addition, existence and uniqueness of the solution will prove. Some numerical examples will solve to test the validity of the method and the given theorems. A comparison of ADM solution with exact and numerical methods are given.
Abstract: In this paper, Adomian decomposition method (ADM) will apply to solve nonlinear fractional differential equations (FDEs) of Caputo sense. These type of equations is very important in engineering applications such as electrical networks, fluid flow, control theory and fractals theory. ADM give analytical solution in form of series solution so the co...
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Circular Distance-Two Labelling of Book Graphs Related to Code Assignment in Computer Wireless Networks
Issue:
Volume 6, Issue 4, December 2021
Pages:
120-124
Received:
7 October 2021
Accepted:
1 November 2021
Published:
10 November 2021
Abstract: Let d be a positive real number. An L(1,d)-labeling of a graph G is an assignment of nonnegative real numbers to the vertices of G such that the adjacent vertices are assigned two different numbers (labels) whose difference is at least one, and the difference between numbers (labels) for any two distance-two vertices is at least d. The minimum range of labels over all L(1,d)-labelings of a graph G is called the L(1,d)-labeling number of G, denoted by λ(1,d) (G). The L(1,d)-labeling with d≥1 of graph arose from the code assignment problem of computer wireless network and the L(1,d)-labeling with 0(1,d) (G), is the minimum σ such that there exists a circular σ-L(1,d)-labeling of G. In this paper, the code assignment of 3-D computer wireless network is abstracted as the circular L(1,d)-labeling of book graph, and the authors determined the circular L(1,d)-labeling numbers of book graph for any positive real number d≥2 basing on the properties and constructions of book graphs.
Abstract: Let d be a positive real number. An L(1,d)-labeling of a graph G is an assignment of nonnegative real numbers to the vertices of G such that the adjacent vertices are assigned two different numbers (labels) whose difference is at least one, and the difference between numbers (labels) for any two distance-two vertices is at least d. The minimum rang...
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Topological Structure of Fuzzy PU-new Ideal in PU-algebra
Muhammad Shafiq,
Naveed Sheikh,
Dawood Khan
Issue:
Volume 6, Issue 4, December 2021
Pages:
125-130
Received:
6 November 2021
Accepted:
17 December 2021
Published:
31 December 2021
Abstract: In this manuscript, we consider the fuzzification of the notion PU-new ideal of PU-algebra and define the fuzzy topological terms such that fuzzy topology, τ-open fuzzy set, fuzzy neighborhood, fuzzy interior, sequence of fuzzy sets, fuzzy neighborhood system, fuzzy continuity of a function with respect to PU-new ideal of PU-algebra. We explore the new theorems and related properties of above mention notions with respect to PU-new ideal on PU-algebras. Such that for (Ⱬ, τ) to be a TSFP on Ⱬ and the set Ḟ is a fuzzy in Ⱬ and NḞ be a fuzzy neighborhood system of Ḟ then the finite intersection of elements of ‘NḞ’ is also an element of ‘NḞ’ also any fuzzy set of Ⱬ which contains an element of “NḞ” is also an element of “NḞ”. Furthermore we prove the conditions with respect to fuzzy neighborhood, convergence of a sequence of fuzzy sets, fuzzy interior set of a fuzzy set under which a fuzzy set Ḟ is τ-open. We show that how the function Ψ from (Ⱬ1,τ) to (Ⱬ2,ω) is fuzzy continuous. We prove that if Ψ is a fuzzy continuous function then for every fuzzy set Ḟ in Ⱬ1, inverse of each neighborhood of Ψ(Ḟ) is a neighborhood of a fuzzy set Ḟ.
Abstract: In this manuscript, we consider the fuzzification of the notion PU-new ideal of PU-algebra and define the fuzzy topological terms such that fuzzy topology, τ-open fuzzy set, fuzzy neighborhood, fuzzy interior, sequence of fuzzy sets, fuzzy neighborhood system, fuzzy continuity of a function with respect to PU-new ideal of PU-algebra. We explore the...
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