On stability of nonlocal neutral stochastic integro differential equations with random impulses and Poisson jumps

• Autores: Sahar M. A. Maqbol, R. S. Jain, B. S. Reddy
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 2, 2023, págs. 211-229
• Idioma: inglés
• DOI: 10.56754/0719-0646.2502.211
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Este artículo examina la existencia y estabilidad de Hyers-Ulam de ecuaciones integrodiferenciales con retardo no-locales aleatorias impulsivas neutrales estocásticas con saltos de Poisson. Inicialmente probamos la existencia de soluciones mild de las ecuaciones usando el teorema del punto fijo de Banach. Luego, investigamos la estabilidad a través de la dependencia continua de las soluciones respecto del valor inicial. A continuación, estudiamos resultados acerca de la estabilidad de Hyers-Ulam bajo la condición de Lipschitz en un intervalo cerrado y acotado. Finalmente, damos un ejemplo ilustrativo de nuestro resultado principal.

  • English

    Abstract This article aims to examine the existence and Hyers-Ulam stability of non-local random impulsive neutral stochastic integrodifferential delayed equations with Poisson jumps. Initially, we prove the existence of mild solutions to the equations by using the Banach fixed point theorem. Then, we investigate stability via the continuous dependence of solutions on the initial value. Next, we study the Hyers-Ulam stability results under the Lipschitz condition on a bounded and closed interval. Finally, we give an illustrative example of our main result.

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