On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative

• Published in: Chaos, solitons and fractals Vol. 143; p. 110557
• Main Authors: Sutar, Sagar T., Kucche, Kishor D.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2021
• Subjects: Atangana-Baleanu-Caputo fractional derivative; Comparison results; Existence and uniqueness; Fractional differential inequalities; Hybrid fractional differential equations; Maximal and minimal solutions; Atangana-Baleanu-Caputo fractional derivative; Comparison results; Hybrid fractional differential equations; 34A12; 26A33; 34A99; 34A40; 35B50; Existence and uniqueness; Fractional differential inequalities; Maximal and minimal solutions
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2020.110557

•We construct the equivalent fractional integral equation and establish the existence results through it.•we build up the theory of inequalities for ABC–hybrid fractional differential equations•The uniqueness, existence of a maximal and minimal solution and the comparison results are obtained through the acquired hybrid fractional inequalities.•Fractional integral inequalities and comparison results acquired in the present paper can utilized to analyze the various qualitative and quantitative properties of solutions for a different class of ABC–hybrid FDEs subject to enhanced initial and boundary conditions In this paper, we develop the theory of nonlinear hybrid fractional differential equations involving Atangana-Baleanu-Caputo (ABC) fractional derivative. We construct the equivalent fractional integral equation and establish the existence results through it. Further, we build up the theory of inequalities for ABC-hybrid fractional differential equations and use it to examine the uniqueness, existence of a maximal and minimal solution and the comparison results.