Difference inequalities of fractional order
DOI:
https://doi.org/10.4067/S0716-09172013000300001Keywords:
Finite difference, Inequality, Fractional order.Abstract
In this paper, we establish some new difference inequalities of fractional order which provide explicit bounds on unknown functions and can be used as an effective tool in the development of the theory of fractional order difference equations.References
[1] Agarwal, R. P. Difference equations and inequalities, Marcel Dekker, New York, (1992).
[2] Atsushi Nagai An integrable mapping with fractional difference, J. Phys. Soc. Jpn. 72, pp. 2181-2183, (2003).
[3] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities, Communications in Applied Analysis, 14, Number 1, pp. 89 - 98, (2010).
[4] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Bihari type, Communications in Applied Analysis, 14, Number 4, pp. 343 - 354, (2010).
[5] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Bihari type, Acta Et Commentationes Universitatis Tartuensis De Mathematica, 17, Number 1, pp. 19 - 30, (2013).
[6] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Some New Fractional Difference Inequalities of Gronwall - Bellman Type, Mathematical Sciences, doi: 10.1186/2251-7456-6-69.
[7] Diaz, J. B. and Osler, T. J. Differences of fractional order, Math.Comp., 28, pp. 185-201, (1974).
[8] Hirota, R. Lectures on difference equations, Science-sha, (2000) (in Japanese).
[9] Jagan Mohan, J. and Deekshitulu, G. V. S. R. Fractional Order Difference Equations, International Journal of Differential Equations, Volume 2012, Article ID 780619, 11 Pages, doi: 10.1155/2012/780619.
[10] Jagan Mohan, J. and Deekshitulu, G. V. S. R. Fractional Difference Inequalities of Gronwall Bellman Bihari Type, International Journal of Pure and Applied Mathematics, 84, Number 3, pp. 175 - 183, (2013).
[11] Lakshmikantham, V. and Leela, S. Differential and integral inequalities, Volume I, Academic Press, New York, (1969).
[12] Pachpatte, B. G. Integral and finite difference inequalities and applications, Elsevier, The Netherlands, (2006).
[13] Podlubny, I Fractional differential equations, Academic Press, San Diego, (1999).
[2] Atsushi Nagai An integrable mapping with fractional difference, J. Phys. Soc. Jpn. 72, pp. 2181-2183, (2003).
[3] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities, Communications in Applied Analysis, 14, Number 1, pp. 89 - 98, (2010).
[4] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Bihari type, Communications in Applied Analysis, 14, Number 4, pp. 343 - 354, (2010).
[5] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Fractional difference inequalities of Bihari type, Acta Et Commentationes Universitatis Tartuensis De Mathematica, 17, Number 1, pp. 19 - 30, (2013).
[6] Deekshitulu, G. V. S. R. and Jagan Mohan, J. Some New Fractional Difference Inequalities of Gronwall - Bellman Type, Mathematical Sciences, doi: 10.1186/2251-7456-6-69.
[7] Diaz, J. B. and Osler, T. J. Differences of fractional order, Math.Comp., 28, pp. 185-201, (1974).
[8] Hirota, R. Lectures on difference equations, Science-sha, (2000) (in Japanese).
[9] Jagan Mohan, J. and Deekshitulu, G. V. S. R. Fractional Order Difference Equations, International Journal of Differential Equations, Volume 2012, Article ID 780619, 11 Pages, doi: 10.1155/2012/780619.
[10] Jagan Mohan, J. and Deekshitulu, G. V. S. R. Fractional Difference Inequalities of Gronwall Bellman Bihari Type, International Journal of Pure and Applied Mathematics, 84, Number 3, pp. 175 - 183, (2013).
[11] Lakshmikantham, V. and Leela, S. Differential and integral inequalities, Volume I, Academic Press, New York, (1969).
[12] Pachpatte, B. G. Integral and finite difference inequalities and applications, Elsevier, The Netherlands, (2006).
[13] Podlubny, I Fractional differential equations, Academic Press, San Diego, (1999).
How to Cite
[1]
J. J. Mohan and G. S. Deekshitulu, “Difference inequalities of fractional order”, Proyecciones (Antofagasta, On line), vol. 32, no. 3, pp. 199-213, 1.
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