Comparison theorems on fractional order difference equations
DOI:
https://doi.org/10.4067/S071609172013000100003Keywords:
Difference equation, Under function, Over function, Fractional order.Abstract
One of the most efficient methods of obtaining information on the behaviour of solutions of difference equations, even when they cannot be solved explicitly, is the comparison principle. In general, the comparison principle is concerned with estimating a function satisfying a difference inequality by the solution of the corresponding difference equation. In the present paper, we shall establish various forms of the principle for fractional order difference equations.References
[1] Agarwal, R. P. Difference equations and inequalities, Marcel Dekker, New York, (1992).
[2] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities, Communications in Applied Analysis, 14 (2010), No. 1, pp. 89  98.
[3] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Bihari type, Communications in Applied Analysis, 14 (2010), No. 4, pp. 343  354.
[4] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Volterra type, International Journal of Pure and Applied Mathematics, 70 (2011), No. 2, pp. 137  149.
[5] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Opial type and initial value problem, Fractional Differential Calculus, 2 (2012), No. 1, pp. 73  86.
[6] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Some New Fractional Difference Inequalities, ICMMSC 2012, CCIS 283 (2012), SpringerVerlag, Berlin, Heidelberg, pp. 403  412.
[7] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Some New Fractional Difference Inequalities of Gronwall  Bellman Type , Mathematical Sciences, Springer Open, Volume 6, Number 69, doi: 10.1186/22517456 669.
[8] Diaz, J. B. and Osler, T. J. Differences of fractional order, Math. Comp., 28, pp. 185201, (1974).
[9] Hirota, R. Lectures on difference equations, Sciencesha, 2000 (in Japanese).
[10] Nagai, A. An integrable mapping with fractional difference, J. Phys. Soc. Jpn. 72, pp. 21812183, (2003).
[11] Pachpatte, B. G. Inequalities of finite difference equations, Marcel Dekker, New York, (2002).
[12] Podlubny, I Fractional differential equations, Academic press, San Diego, (1999).
[13] S. Sugiyama Comparison theorems on difference equations, Bull. Sci. Engr. Research Lab., Waseda Univ., 47, pp. 7782, (1970).
[2] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities, Communications in Applied Analysis, 14 (2010), No. 1, pp. 89  98.
[3] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Bihari type, Communications in Applied Analysis, 14 (2010), No. 4, pp. 343  354.
[4] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Volterra type, International Journal of Pure and Applied Mathematics, 70 (2011), No. 2, pp. 137  149.
[5] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Opial type and initial value problem, Fractional Differential Calculus, 2 (2012), No. 1, pp. 73  86.
[6] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Some New Fractional Difference Inequalities, ICMMSC 2012, CCIS 283 (2012), SpringerVerlag, Berlin, Heidelberg, pp. 403  412.
[7] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Some New Fractional Difference Inequalities of Gronwall  Bellman Type , Mathematical Sciences, Springer Open, Volume 6, Number 69, doi: 10.1186/22517456 669.
[8] Diaz, J. B. and Osler, T. J. Differences of fractional order, Math. Comp., 28, pp. 185201, (1974).
[9] Hirota, R. Lectures on difference equations, Sciencesha, 2000 (in Japanese).
[10] Nagai, A. An integrable mapping with fractional difference, J. Phys. Soc. Jpn. 72, pp. 21812183, (2003).
[11] Pachpatte, B. G. Inequalities of finite difference equations, Marcel Dekker, New York, (2002).
[12] Podlubny, I Fractional differential equations, Academic press, San Diego, (1999).
[13] S. Sugiyama Comparison theorems on difference equations, Bull. Sci. Engr. Research Lab., Waseda Univ., 47, pp. 7782, (1970).
Published
20130623
How to Cite
[1]
J. Jagan and G. S. Deekshitulu, “Comparison theorems on fractional order difference equations”, Proyecciones (Antofagasta, On line), vol. 32, no. 1, pp. 3146, Jun. 2013.
Issue
Section
Artículos

Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
 No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.