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

• Alka Chadha ^[1] ; Dwijendra N Pandey ^[1]
  1. [1] Indian Institute of Technology Roorkee Department of Mathematics
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 17, Nº. 1, 2015, págs. 11-27
• Idioma: inglés
• DOI: 10.4067/S0719-06462015000100002
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

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