Local and extremal solutions of some fractional integrodifferential equation with impulses

Year 2013, Volume: 62 Issue: 1, 101 - 113, 01.02.2013

Atmania Rahima

https://doi.org/10.1501/Commua1_0000000689

Abstract

LOCAL AND EXTREMAL SOLUTIONS OF SOME FRACTIONAL INTEGRODIFFERENTIAL EQUATION WITH IMPULSES

Abstract

The subject of this work is to prove existence, uniqueness, and continuous dependence upon the data of solution to integrodifferential hyperbolic
equation with integral conditions. The proofs are based on a priori estimates
and Laplace transform method. Finally, the solution by using a numerical
technique for inverting the Laplace transforms is obtained.

Keywords

Local existence, extremal solution, integrodiğerential equation, Caputo fractional derivative, impulsive conditions, …xed point theory, impulsive fractional inequality

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• Current address : LMA, Department of Mathematics, University of Badji-Mokhtar, Annaba