TY  - JOUR
AU  - Souid, Mohammed Said
AU  - Bouazza, Zoubida
AU  - Günerhan, Hatıra
AU  - Maazouz, Kadda
AU  - Bensaid, M'hamed
AU  - Arab, Meraa
PY  - 2026
TI  - Lyapunov stability and solvability of nonlocal fractional differential equations with generalized katugampola derivative
JO  - AIMS Mathematics
SP  - 17766
EP  - 17793
VL  - 11
IS  - 6
AB  - This paper investigates a class of fractional differential equations (FDEs) that involve the generalized Katugampola fractional derivative (FD) subject to nonlocal boundary conditions. By transforming the considered boundary value problems (BVPs) into equivalent integral equations, we establish several results concerning the existence and uniqueness of solutions. The analysis is carried out using classical fixed point (FP) techniques, including the Banach contraction principle(BC), as well as Schaefer's FP theorems under appropriate assumptions. In addition, we examine the Lyapunov stability of nontrivial solutions and derive sufficient conditions to ensure asymptotic stability. The obtained results extend and complement the existing contributions in the literature on fractional BVPs with nonlocal conditions. Finally, illustrative examples are provided to demonstrate the applicability of the theoretical findings.
UR  - https://doi.org/10.3934/math.2026724
DO  - 10.3934/math.2026724