Malaysian Journal of Mathematical Sciences, September 2023, Vol. 17, No. 3
Variable-order Implicit Fractional Differential Equations based on the Kuratowski MNC Technique
Bouazza, Z., Souid, M. S., Hussin, C. H. C., Mandangan, A., and Sabit, S.
Corresponding Email: haziqah@ums.edu.my
Received date: 11 February 2023
Accepted date: 30 May 2023
Abstract:
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 non-compactness (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.
Keywords: fractional differential equations of variable order; boundary value problem; Darbo's fixed point theorem; measure of non-compactness; Ulam Hyers Rassias stability; Green function
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