Buradasınız

Solutions of Perturbed Nonlinear Nabla Fractional Difference Equations of Order 0 < < 1

Journal Name:

Publication Year:

Abstract (2. Language): 
The present paper provides methods and suitable criterion that de- scribe the nature and behavior of solutions of nabla fractional difference equations of order 0 < < 1, without actually constructing or approx- imating them. Since the existence and uniqueness of solutions of nabla discrete fractional order initial value problems is already guaranteed, we begin with the continuous dependence on the initial conditions and pa- rameters. Next we develop a nonlinear variation of parameters formula and give an example.
139-150

REFERENCES

References: 

[1] Agarwal, R.P. Difference equations and inequalities, Marcel Dekker, New
York, 1992.
[2] Alekseev, V.M. An estimate for the perturbations of the solutions of or-
dinary differential equations, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 2
(1961), 28 - 36.
[3] Deekshitulu, G.V.S.R. and Jagan Mohan, J. Discrete fractional calculus,
Rev. Bull. Cal. Math. Soc, 19 (2011), No. 2, 173 - 184.
[4] Deekshitulu, G.V.S.R. and Jagan Mohan, J. Fractional difference inequal-
ities, Communications in Applied Analysis, 14 (2010), No. 1, 89 - 98.
150 G.V.S.R.Deekshitulu and J.Jagan Mohan
[5] Deekshitulu, G.V.S.R. and Jagan Mohan, J. Some new fractional dif-
ference inequalities, ICMMSC 2012, CCIS 283 (2012), Springer-Verlag,
Berlin, Heidelberg, 403 - 412.
[6] Diaz, J.B. and Osler, T.J. Differences of fractional order, Math. Comp.,
28 (1974), 185 - 201.
[7] Hirota, R. Lectures on difference equations, Science-sha, 2000 (in
Japanese).
[8] Lakshmikantham, V. and Deo, S.G. Method of Variation of Parameters
for Dynamic Systems, Gordon and Breach, Amsterdam, 1998.
[9] Lakshmikantham, V. and Leela, S. Differential and integral inequalities,
Vol. I, Academic Press, New York, 1969.
[10] Lakshmikantham, V. and Trigiante, D. Theory of difference equations,
Academic Press, New York, 1988.
[11] Nagai, A. An integrable mapping with fractional difference, J. Phys. Soc.
Jpn., 72 (2003), 2181 - 2183.
[12] Pachpatte, B.G. Inequalities of finite difference equations, Marcel Dekker,
New York, 2002.
[13] Podlubny, I Fractional differential equations, Academic Press, San Diego,
1999.

Thank you for copying data from http://www.arastirmax.com