Accepted for publication in JNEEA

Existence uniqueness of mild solution and approximate controllability of fractional evolution equations with deformable fractional derivative

A. Meraj, D. N. Pandey

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India, Pin-247667

Received on October 21, 2017
Accepted on September 14, 2018

Communicated by Gaston M. N'Guérékata

Abstract.  This article is concerned with the existence and uniqueness of mild solution, and approximatecontrollability of evolution equations with deformable fractional derivative. The results are obtained with the help of semigroup theory, Banach fixed point theorem, and Schauder fixed point theorem.
Keywords: Deformable fractional derivative, Banach fixed point theorem, Schauder fixed point theorem, semigroup theory, approximate controllability.
2010 Mathematics Subject Classification:   93B05; 34A08; 34A12; 34K30.

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