Numerical investigation of pine wilt disease using fractal–fractional operator

This work investigates a conspicuous disease of pine trees known as pine wilt disease (PWD). This disease propagates through a pine wilt nematode, a microscopical ringworm that mainly contaminates the pine trees of the Pinus genus. Its development way comprises many stages. Pine trees impacted by PWD initially show yellow-colored leaves and then turn reddish brown after some time. The pine sawyer beetles act as conveyors that transfer the pine wilt nematode. The disease in the frame of the PWD model is studied with fractal–fractional (FF) derivatives in the context of Caputo and Caputo–Fabrizio (CF) derivatives under different fractional order \({\partial_{1}}\) ${\partial }_1$ and fractal dimension \({\partial_{2}}\) ${\partial }_2$ values. Here, the fundamental characteristics of the given model are discussed. The fixed point theory’s theoretical results are interpreted for existence and uniqueness, while Ulam–Hyres (UH) stability is also presented for the given model. Further, the Caputo and CF derivative-based numerical schemes are also displayed. After analyzing the numerical simulations, it is found that the FF operator is more capable of analyzing the PWD model.