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Cubo (Temuco)
On-line version ISSN 0719-0646
Cubo vol.22 no.3 Temuco Dec. 2020 Epub Dec 23, 2020
http://dx.doi.org/10.4067/S0719-06462020000300325
Articles
Existence and Attractivity Theorems for Nonlinear Hybrid Fractional Integrodifferential Equations with Anticipation and Retardation
1Kasubai, Gurukul Colony, Thodga Road, Ahmedpur-413 515, Dist. Latur, Maharashtra, India. E-mail: bcdhage@gmail.com
In this paper, we establish the existence and a global attractivity results for a nonlinear mixed quadratic and linearly perturbed hybrid fractional integrodifferential equation of second type involving the Caputo fractional derivative on unbounded intervals of real line with the mixed arguments of anticipations and retardation. The hybrid fixed point theorem of Dhage is used in the analysis of our nonlinear fractional integrodifferential problem. A positivity result is also obtained under certain usual natural conditions. Our hypotheses and claims have also been explained with the help of a natural realization.
Keywords and Phrases: Hybrid fractional integrodifferential equation; Dhage fixed point theorem; Existence theorem; Attractivity of solutions; Asymptotic stability
En este artículo, se establecen resultados de existencia y de atractividad global para una ecuación no lineal cuadrática mixta e híbrida fraccionaria integrodiferencial linealmente perturbada de segundo tipo involucrando la derivada fraccional de Caputo en intervalos no acotados de la recta real con argumentos mixtos de anticipación y retardo. El teorema de punto fijo híbrido de Dhage es usado en el análisis de nuestro problema no lineal fraccionario integrodiferencial. También se obtiene un resultado de positividad bajo ciertas condiciones naturales usuales. Nuestras hipótesis y afirmaciones también se explican con la ayuda de una realización natural.
Acknowledgement
The author is thankful to the referees for giving some suggestions for the improvement of this paper.
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Received: May 20, 2020; Accepted: October 22, 2020
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