<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Weighted pseudo almost automorphic functions with applications to impulsive fractional integro-differential equation

Department of Mathematics, School of Sciences, Arts, Media & Management

Department of Mathematics, School of Arts, Science and Humanities

Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This paper’s main motivation is to study the notion of weighted pseudo almost automorphic (𝒲𝒫𝒜𝒜) functions and establish the existence results of piecewise...

Weighted pseudo almost automorphic functions with applications to impulsive fractional integro-differential equation

Publicado en línea: 04 feb 2023

Páginas: 143 - 166

DOI: https://doi.org/10.2478/auom-2023-0007

Palabras clave
Integro-differential equation, Fractional order differential equation, Impulsive conditions, Weighted pseudo almost automorphic function

© 2023 Velusamy Kavitha et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Weighted pseudo almost automorphic functions with applications to impulsive fractional integro-differential equation

Publicado en línea: 04 feb 2023

Páginas: 143 - 166

DOI: https://doi.org/10.2478/auom-2023-0007

Palabras claveIntegro-differential equation, Fractional order differential equation, Impulsive conditions, Weighted pseudo almost automorphic function

© 2023 Velusamy Kavitha et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Palabras clave
Integro-differential equation, Fractional order differential equation, Impulsive conditions, Weighted pseudo almost automorphic function