Existence and Attractivity Theorems for Nonlinear Hybrid Fractional Integrodifferential Equations with Anticipation and Retardation

Bapurao C. Dhage

doi:10.4067/S0719-06462020000300325

DOI:

https://doi.org/10.4067/S0719-06462020000300325

Abstract

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

Hybrid fractional integrodifferential equation , Dhage fixed point theorem , Existence theorem , Attractivity of solutions , Asymptotic stability

Bapurao C. Dhage Kasubai, Gurukul Colony, Thodga Road, Ahmedpur-413 515, Dist. Latur, Maharashtra, India.

Pages: 325–350
Date Published: 2020-12-07
Vol. 22 No. 3 (2020)

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