| Summary: | In this paper, we investigate the Darboux problem of conformable partial differential equations (DPCDEs) using fixed point theory. We focus on the existence and Ulam–Hyers–Rassias stability (UHRS) of the solutions to the problem, which requires finding solutions to nonlinear partial differential equations that satisfy certain boundary conditions. Using fixed point theory, we establish the existence and uniqueness of solutions to the DPCDEs. We then explore the UHRS of the solutions, which measures the sensitivity of the solutions to small perturbations in the equations. We provide three illustrative examples to demonstrate the effectiveness of our approach.
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