Abstract
In this paper, we obtain sufficient conditions for the existence and uniqueness results of the pantograph fractional differential equations (FDEs) with nonlocal conditions involving Atangana–Baleanu–Caputo (ABC) derivative operator with fractional orders. Our approach is based on the reduction of FDEs to fractional integral equations and on some fixed point theorems such as Banach’s contraction principle and the fixed point theorem of Krasnoselskii. Further, Gronwall’s inequality in the frame of the Atangana–Baleanu fractional integral operator is applied to develop adequate results for different kinds of Ulam–Hyers stabilities. Lastly, the paper includes an example to substantiate the validity of the results.
Highlights
Fractional calculus (FC) has been growing quicker during the most recent few years, and numerous phenomena having the power-law impact have been described precisely with fractional models [1,2,3,4,5,6,7,8,9]
Recent investigations of the existence and uniqueness of solutions for fractional differential equations (FDEs) of the impulsive, evolution, and functional problems with initial or boundary conditions can be found within the following research series [27,28,29,30] and the references therein
Not many works have been proposed for pantograph FDEs, especially those involving ABC fractional operator and nonlocal conditions
Summary
Fractional calculus (FC) has been growing quicker during the most recent few years, and numerous phenomena having the power-law impact have been described precisely with fractional models [1,2,3,4,5,6,7,8,9]. Recent investigations of the existence and uniqueness of solutions for fractional differential equations (FDEs) of the impulsive, evolution, and functional problems with initial or boundary conditions can be found within the following research series [27,28,29,30] and the references therein. Not many works have been proposed for pantograph FDEs, especially those involving ABC fractional operator and nonlocal conditions.
Sign-in/Register to view highlights & summary 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.
