Properties of Some Dynamic Partial Integrodifferential Equations on Time Scales

Authors

  • Deepak B. Pachpatte Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, Maharashtra

DOI:

https://doi.org/10.26713/cma.v9i4.591

Keywords:

Explicit estimate, Integral inequality, Two variables, Time scales

Abstract

The main objective of this paper is to study some properties of new dynamic equations partial integrodifferential equations in two independent variables on time scales. The tools used in obtaining our results are application of Banach Fixed point theorem. We also used dynamic inequality with explicit estimates to study the properties of solution of dynamic partial integrodifferential equation.

Downloads

Download data is not yet available.

References

R. Agarwal, D. O'Regan and S. Saker, Dynamic Inequalities on Time Scales, Springer (2014), DOI: 10.1007/978-3-319-11002-8.

G. Anastassiou, Frontiers in Time Scales and Inequalities, World Scientific Publishing Company (2015), DOI: 10.1142/9711.

M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkhauser, Boston ” Berlin (2001), DOI: 10.1007/978-1-4612-0201-1.

M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston ” Berlin (2003), DOI: 10.1007/978-0-8176-8230-9.

E. Akin-Bohner, M. Bohner and F. Akin, Pachpatte inequalities on time scales, J. Inequal. Pure Appl. Math. 7(4) (2006), 1 – 8.

J. Gu and F. Meng, Some new nonlinear Volterra-Fredholm type dynamic integral inequalities on time scales, Appl. Math. Comput. 245 (2014), 235 – 242, DOI: 10.1016/j.amc.2014.07.056.

S. Hilger, Analysis on Measure chain-A unified approach to continuous and discrete calculus, Results. Math. 18(1) (1990), 18 – 56, DOI: 10.1007/BF03323153.

F. Meng and J. Shao, Some new Volterra-Fredholm type dynamic integral inequalities on time scales, Appl. Math. Comput. 223 (2013), 444 – 451, DOI: 10.1016/j.amc.2013.08.025.

E. Messina1 and A. Vecchio, Stability and convergence of solutions to Volterra integral equations on time scales, Discrete Dyn. Nat. Soc. 2015 (2015), Art. 612156, 6 pages, DOI: 10.1155/2015/612156.

E. Messina, E. Russo and A. Vecchio, Volterra integral equations on time scales: stability under constant perturbations via Liapunov direct method, Ric. Mat. 64 (2015), 345 – 355, DOI: 10.1007/511587-01-0243-4.

D.B. Pachpatte, Some dynamic inequalities applicable to partial integrodifferential equations on time scales, Arch. Math. 51(3) (2015), 143 – 152, DOI: 10.5817/AM2015-3-143.

D.B. Pachpatte, Estimates of certain iterated dynamic inequalities on time scales, Qual. Theory Dyn. Syst. 13(2) (2014), 353 – 362, DOI: 10.1007/s12346-014-0120-1.

Downloads

Published

26-09-2018
CITATION

How to Cite

Pachpatte, D. B. (2018). Properties of Some Dynamic Partial Integrodifferential Equations on Time Scales. Communications in Mathematics and Applications, 9(4), 489–498. https://doi.org/10.26713/cma.v9i4.591

Issue

Section

Research Article