J. Nonl. Evol. Equ. Appl. 2018 (4), pp. 39-55, published on August 2, 2019:

Doubly weighted pseudo almost automorphic solutions for two-term fractional order differential equations

V. Singh, D. N. Pandey

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

Received on May 12, 2017, revised version on March 5, 2018
Accepted on March 7, 2018

Communicated by Khalil Ezzinbi

Abstract.  In this paper, we investigate the existence and uniqueness of doubly weighted pseudo almost automorphic mild solutions with Stepanov like doubly weighted pseudo almost automorphic forcing term using two non-equivalent weight functions for two-term fractional differential equations. In this paper, we will use the notion of Weyl fractional derivative, generalized semigroup theory for linear operators and fractional calculus techniques to obtain the main results.
Keywords:Generalized semigroup theory, Weyl fractional derivative, sectorial operator, weighted pseudo almost automorphic and double weighted pseudo almost automorphic functions, double weighted pseudo Stepanov like almost automorphic functions.
2010 Mathematics Subject Classification:   43A60, 34A08, 34G10, 35R11, 35R60, 45N05, 47D06.

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