Variable-order Implicit Fractional Differential Equations based on the Kuratowski MNC Technique - Bouazza, Z; Souid, M. S.; Che Haziqah Che Hussin; Arif Mandangan; Sabit, S. (Institute for Mathematical Research, Universiti Putra Malaysia, 2023)
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.