Qualitative Analysis for Nonlinear Fractional Differential Equations With <i>p</i> ‐Laplacian Operator

ABSTRACT In this manuscript, the ‐Laplacian operator is employed to study a class of general nonlinear fractional differential equations. The primary objective of this work is to establish existence and uniqueness results, together with an analysis of Hyers–Ulam stability, for nonlinear fractional differential equations involving the ‐Laplacian operator and fractional derivatives of different orders. To achieve these results, the proposed equations are first transformed into equivalent integral formulations using appropriate Green's functions. The existence and uniqueness of solutions are then investigated using fixed point techniques, while uniqueness is further ensured via the Banach contraction mapping principle. In addition, tools from functional analysis and dynamical systems theory are employed to examine the Hyers–Ulam stability of the problem. Finally, with the process innovation a representative example is provided to demonstrate the applicability and effectiveness of the obtained results.