Existence results for fractional neutral differential inclusion via deformable fractional derivative in Banach spaces

K.M. Anjitha; V. Kavitha; Seenith Sivasundaram; M. Mallika Arjunan

K.M. Anjitha chool of Sciences, Arts, Media \& Management, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India.
V. Kavitha School of Sciences, Arts, Media \& Management, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India.
Seenith Sivasundaram College of Engineering, Science and Mathematics, Daytona Beach, FL 32114, USA.
M. Mallika Arjunan School of Arts, Science and Humanities, SASTRA Deemed to be University, Thanjavur-613401, Tamil Nadu, India.

Abstract

The purpose of this paper is to establish the existence results for fractional neutral differential inclusion [$\p$] via deformable fractional derivative [$\d$] in Banach spaces. The investigation is valid for both convex and non-convex values in the set-valued (multi-valued) function. Additionally, we provide applications of our abstract theory as examples to support our findings.