Weighted pseudo almost automorphic solutions of fractional functional differential equations

• Syed Abbas ^[1]
  1. [1] Indian Institute of Technology Mandi School of Basic Sciences
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 16, Nº. 1, 2014, págs. 21-36
• Idioma: inglés
• DOI: 10.4067/S0719-06462014000100003
• Enlaces
  • Texto completo
• Resumen
  • español

    En este artículo discutimos la existencia de una solución seudo casi automórfica con peso de ecuaciones diferenciales funcionales de orden fraccional. Usando el teorema del punto fijo, establecemos la existencia y unicidad de la solución del problema en estudio. Los resultados obtenidos extienden la teoría de soluciones casi automórficas a clases más generales de soluciones seudo casi automórficas con peso. Estas extensiones permiten estudiar dinámicas infinito-dimensional como la onda fraccionaria y la ecuación del calor, las cuales se presentan en este artículo. Al final, mostramos varios ejemplos para ilustrar los resultados analíticos obtenidos.

  • English

    In this paper we discuss the existence of weighted pseudo almost automorphic solution of fractional order functional differential equations. Using the fixed point theorem we establish existence and uniqueness of solution to the problem under consideration. The results obtained extend the theory of almost automorphic solutions to a more general class of weighted pseudo almost automorphic solutions. These extensions allow to treat infinite dimensional dynamics such as fractional wave and heat equation which are presented in the paper. At the end we give several example to illustrate the analytical findings.

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