ON THE HIGHER-ORDER Λ-FRACTIONAL BENDING BEAM

This work extends the [Formula: see text]-fractional model for Euler–Bernoulli bending beams. By generalizing the model to higher orders, the fundamental fractional equations of the structure can be derived directly from the applied load and the higher-order governing equation rather than relying on a known bending moment. The [Formula: see text]-fractional is formulated utilizing the Riemann–Liouville derivative and the definition of fractional space gradient, which provides a well-defined curvature. The fractional form of the beam’s deflection is introduced in fractional [Formula: see text]-space and is mapped to conventional coordinates, yielding a closed-form solution. This approach requires mean values and interpolation to obtain the deflection response. Static analysis of pinned-supported and indeterminate fixed-supported beams under typical distributed loads and boundary conditions is presented and discussed. The findings demonstrate that varying the fractional parameter has a significant impact on the deformation characteristics of flexural beams. Verification shows that the fractional model converges to the classical Euler–Bernoulli beam behavior as the fractional parameter approaches an integer value.