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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.17 no.1 Temuco  2015

http://dx.doi.org/10.4067/S0719-06462015000100002 

Periodic BVP for a class of nonlinear differential equation with a deviated argument and integrable impulses

Alka Chadha and Dwijendra N Pandey
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India -247667 alkachaddha03@gmail.com, dwij.iitk@gmail.com


ABSTRACT
This paper deals with periodic BVP for integer/fractional order differential equations with a deviated argument and integrable impulses in arbitrary Banach space X for which the impulses are not instantaneous. By utilizing fixed point theorems, we firstly establish the existence and uniqueness of the mild solution for the integer order differential system and secondly obtain the existence results for the mild solution to the fractional order differential system. Also at the end, we present some examples to show the effectiveness of the discussed abstract theory.

Keywords and Phrases: Deviating arguments, Fixed point theorem, Impulsive differential equation, Periodic BVP, Fractional calculus.
2010 AMS Mathematics Subject Classification: 34G20, 34K37, 34K45, 35R12, 45J05.


RESUMEN
Este artículo estudia las ecuaciones diferenciales de orden entero/fraccional con condiciones de frontera periódicas con un argumento desviado e impulsos integrables en espacios de Banach arbitrarios X donde los pulsos no son instantáneos. Utilizando teoremas de punto fijo, establecemos la existencia y unicidad de soluciones temperadas para los sistemas diferenciales de orden entero, y luego obtenemos resultados de existencia para soluciones temperadas del sistema diferencial de orden fraccional. Además, presentamos un ejemplo para mostrar la efectividad de la teoría abstracta discutida.

 


 

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Received: December 2014. Accepted: January 2015.

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