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On the solution of T -controllable abstract fractional differential equations with impulsive effects

  • Autores: Ganga Ram Gautam, Sandra Pinelas, Manoj Kumar, Namrata Arya, Jaimala Bishnoi
  • Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 3, 2023, págs. 363-386
  • Idioma: inglés
  • DOI: 10.56754/0719-0646.2503.363
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  • Resumen
    • español

      Resumen En este artículo de investigación, delimitamos la definición de solución mild para ecuaciones diferenciales fraccionarias con retardo dependiente del estado (AFDEw/SDD) de orden α ∈ (1, 2) con efectos impulsivos y comparamos la solución con aquellas de ecuaciones diferenciales impulsivas de segundo orden. Además obtenemos condiciones suficientes para la existencia de soluciones mild de inclusiones funcionales diferenciales fraccionales instantánea y no-instantáneamente impulsivas con retardo dependiente del estado (IFDIw/SDD) usando la teoría de punto fijo multivaluados y técnicas de operadores. Más aún, estudiamos la controlabilidad por trayectoria (T −controlabilidad) de los AFDEw/SDD. Finalmente, presentamos algunos ejemplos para ilustrar las condiciones suficientes que involucran derivadas parciales y ordinarias.

    • English

      Abstract In this research article, we delimitate the definition of mild solution for abstract fractional differential equations with state-dependent delay (AFDEw/SDD) of order α ∈ (1, 2) with impulsive effects and compare the solution to the second-order impulsive differential equations. Further, we obtain sufficient conditions of the existence of mild solution for instantaneous and non-instantaneous impulsive fractional functional differential inclusions with state-dependent delay (IFDIw/SDD) using the multi-valued fixed point theory and operator techniques. Furthermore, we study the trajectory controllability (T −controllability) of the AFDEw/SDD. At last, we present some examples to illustrate the sufficient conditions involving partial and ordinary derivatives.

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Los metadatos del artículo han sido obtenidos de SciELO Chile
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