Undetermined coefficients for local fractional differential equations

1364
Downloads

1418
Views
Authors
Roshdi Khalil
 Department of Mathematics, The University of Jordan, Amman, Jordan.
Mohammed Al Horani
 Department of Mathematics, Faculty of Science, University of Hail, Saudi Arabia.
Douglas Anderson
 Department of Mathematics, Concordia College, Moorhead, MN, USA.
Abstract
Let \(G= (V, \sigma, \mu)\) be a fuzzy graph. Let \(H\) be the graph constructed from \(G\) as follows \(V(H) =V(G)\),
two points \(u\) and \(v\) are adjacent in \(H\) if and only if \(u\) and \(v\) are adjacent and degree fuzzy equitable in
\(G\). \(H\) is called the adjacency inherent fuzzy equitable graph of \(G\) or fuzzy equitable associate graph
of G and is denoted by \(e^{ef}(G)\). In this paper we introduced the concept of fuzzy equitable associate
graph and obtain some interesting results for this new parameter in fuzzy equitable associate graph.
Keywords
 Fuzzy equitable dominating set
 fuzzy equitable associate graph
 preefuzzy equitable graph
 degree equitable fuzzy graph.
MSC
References

[1]
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 5766.

[2]
T. Abdeljawad, M. Al Horani, R. Khalil, Conformable Fractional Semigroups of Operators, J. Semigroup Theory Appl., 2015 (2015 ), 11 pages.

[3]
M. Abu Hammad, R. Khalil, Abel's formula and Wronskian for conformable fractional differential equations, Int. J. Differential Equations Appl., 13 (2014), 177183.

[4]
B. Bayour, D. F. M. Torres, Existence of solution to a local fractional nonlinear differential equation, J. Comput. Appl. Math., 312 (2016), 127133

[5]
N. Benkhettou, S. Hassani, D. F. M. Torres, A conformable fractional calculus on arbitrary time scales, J. King Saud Univ., 28 (2016), 9398.

[6]
T. Caraballoa, M. Abdoul Diopb, A. A. Ndiayeb, Asymptotic behavior of neutral stochastic partial functional integrodifferential equations driven by a fractional Brownian motion, J. Nonlinear Sci. Appl., 7 (2014), 407421.

[7]
A. Gokdogan, E. Unal, E. Celik, Existence and Uniqueness Theorems for Sequential Linear Conformable Fractional Differential Equations, , , (to appear in Miskolc Mathematical Notes.)

[8]
M. Hao, C. Zhai, Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order , J. Nonlinear Sci. Appl., 7 (2014), 131137.

[9]
R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new Definition of Fractional Derivative, J. Comput. Appl. Math., 264 (2014), 6570.

[10]
A. Kilbas, H. Srivastava, J. Trujillo, Theory and applications of fractional differential equations, Math. Studies. Northholland, NewYork (2006)

[11]
K. S. Miller, An introduction to fractional calculus and fractional differential equations, J.Wiley and Sons, New York (1993)

[12]
J. A. Nanware, D. B. Dhaigude, Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions, J. Nonlinear Sci. Appl., 7 (2014), 246254.