Abstract
This note is concerned with establishing existence theory of solutions to a class of implicit fractional differential equations (FODEs) involving nonsingular derivative. By using usual classical fixed point theorems of Banach and Krasnoselskii, we develop sufficient conditions for the existence of at least one solution and its uniqueness. Further, some results about Ulam–Hyers stability and its generalization are also discussed. Two suitable examples are given to demonstrate the results.
Highlights
fractional differential equations (FODEs) have many applications in real world problems; see [1,2,3]
The considered differential operator has been introduced in 2015 by Caputo and Fabrizio [11] (in short, we write it as (CFFD)), which replaces the singular kernel by a nonsingular kernel of exponential type
The stability theory of Ulam–Hyers type has been properly investigated for ordinary FODEs
Summary
FODEs have many applications in real world problems; see [1,2,3]. The concerned area has been investigated from different aspects in the last several years. These investigations include the existence theory of solutions by the fixed point theory, numerical analysis and stability theory by taking Hadamard, Riemann–Liouville, Caputo, etc., type fractional derivatives (for details, see [4,5,6,7]). The existence theory, together with stability results, has been very well investigated for other FODEs; for details, see [8,9,10]. We are using the fixed point theory to obtain some results for the existence and uniqueness of a solution to the considered problem (1).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
