| Summary: | This work proposes a valuable and successful strategy for approximating the solutions to the Bagley–Torvik system, which plays an essential role in fractional calculus. The Caputo sense is used to derive the basic conformable fractional. The Bagley–Torvik problem is numerically solved in this study using an effective symmetric projection method. From this symmetry, there are some interesting original results. The proposed approach has two key benefits. We began by converting the connected fractional Bagley–Torvik equations into two fractional-order Bagley–Torvik equations, which we then solved using the current method. Second, two linear equation systems are solved to obtain approximate solutions.
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