Browsing by Author "Grayna, Jeyakumar"

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Citation - WoS: 8
Citation - Scopus: 15
Measure Pseudo Almost Automorphic Solution To Second Order Fractional Impulsive Neutral Differential Equation
(Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Grayna, Jeyakumar; Kavitha, Velusamy
We discuss the concept of pseudo almost automorphic solution to fractional neutral differential equation with impulses using measure theory. Our principal results are obtained via semigroup theory and the fixed point theorem due to Krasnoselskii and their combination with the properties of measure theory. An example is provided to outline the thought developed on this work.
Citation - WoS: 4
Weighted Pseudo Almost Automorphic Functions With Applications To Impulsive Fractional Integro-Differential Equation
(Ovidius Univ Press, 2023) Arjunan, Mani Mallika; Baleanu, Dumitru; Grayna, Jeyakumar; Kavitha, Velusamy
This paper's main motivation is to study the notion of weighted pseudo almost automorphic (WPAA) functions and establish the existence results of piecewise continuous mild solution of fractional order integro-differential equation with instantaneous impulses. The usual WPAA functions may not work since the solution of impulsive differential equations may not be continuous. Thus in order to give a broader spectrum, we introduce this concept. We establish main results by using the Banach contraction mapping principle and Sadovskii's fixed point theorem. An example is shown to exhibit our analytic findings.