Variable-order Implicit Fractional Differential Equations based on the Kuratowski MNC Technique

• Main Authors: Bouazza, Z, Souid, M. S., Che Haziqah Che Hussin, Arif Mandangan, Sabit, S.
• Format: Article
• Language: English; English
• Published: Institute for Mathematical Research, Universiti Putra Malaysia 2023
• Subjects: Q1-390 Science (General); QA1-43 General
• Online Access: https://eprints.ums.edu.my/id/eprint/38004/1/ABSTRACT.pdf; https://eprints.ums.edu.my/id/eprint/38004/2/FULL%20TEXT.pdf; https://eprints.ums.edu.my/id/eprint/38004/; https://doi.org/10.47836/mjms.17.3.05

In this manuscript, we examine the existence and the stability of solutions to the boundary value problem of Riemann-Liouville fractional differential equations of variable order. The obtained new results are based on the fixed-point theorem of Darbo and Kuratowski’s metric of noncompactness (MNK) with the help of piece-wise constant functions. In addition, the derived fundamental results are proven suitable because they satisfy the Ulam-Hyers Rassias stability sufficient conditions. Several numerical examples were discussed too to demonstrate the reasonableness and effectiveness of the observed results.