Numerical Calculation of Fractional Derivatives for the Sinc Functions via Legendre Polynomials
Abbas
Saadatmandi
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
author
Ali
Khani
Department of Mathematics, Faculty of Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran
author
Mohammad Reza
Azizi
Department of Mathematics, Faculty of Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran
author
text
article
2020
eng
This paper provides the fractional derivatives of the Caputo type for the sinc functions. It allows to use efficient numerical method for solving fractional differential equations. At first, some properties of the sinc functions and Legendre polynomials required for our subsequent development are given. Then we use the Legendre polynomials to approximate the fractional derivatives of sinc functions. Some numerical examples are introduced to demonstrate the reliability and effectiveness of the introduced method.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
2
no.
2020
71
86
http://mir.kashanu.ac.ir/article_96936_06da74b6baa7fbe772ca4a6139f4606c.pdf
dx.doi.org/10.22052/mir.2018.96632.1074
On L(d,1)-labelling of Trees
Irena
Hrastnik
Faculty of Mechanical Engineering,
University of Maribor,
Maribor, Slovenia
author
Janez
Žerovnik
Faculty of Mechanical Engineering,
University of Ljubljana,
Ljubljana, Slovenia
author
text
article
2020
eng
Given a graph G and a positive integer d, an L(d,1)-labelling of G is a function f that assigns to each vertex of G a non-negative integer such that if two vertices u and v are adjacent, then |f(u)-f(v)|>= d and if u and v are at distance two, then |f(u)-f(v)|>= 1. The L(d,1)-number of G, λd(G), is the minimum m such that there is an L(d,1)-labelling of G with f(V)⊆ {0,1,… ,m}. A tree T is of type 1 if λd(T)= Δ +d-1 and is of type 2 if λd(T)>= Δ+d. This paper provides sufficient conditions for λd(T)=Δ+d-1 generalizing the results of Wang [11] and Zhai, Lu, and Shu [12] for L(2,1)-labelling.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
2
no.
2020
87
102
http://mir.kashanu.ac.ir/article_108519_7a815e176ecf64051ff8ea4e1a552bac.pdf
dx.doi.org/10.22052/mir.2020.227370.1211
The Zagreb Index of Bucket Recursive Trees
Ramin
Kazemi
Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran
author
Ali
Behtoei
Department of Pure Mathematics, Imam Khomeini International University, Qazvin, I. R. Iran
author
Akram
Kohansal
Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran
author
text
article
2020
eng
Bucket recursive trees are an interesting and natural generalization of recursive trees. In this model the nodes are buckets that can hold up to b>= 1 labels. The (modified) Zagreb index of a graph is defined as the sum of the squares of the outdegrees of all vertices in the graph. We give the mean and variance of this index in random bucket recursive trees. Also, two limiting results on this index are given.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
5
v.
2
no.
2020
103
111
http://mir.kashanu.ac.ir/article_109509_f3b0cb23045fab361dda93a3b444fa84.pdf
dx.doi.org/10.22052/mir.2020.204312.1166