Fractional Euler–bernoulli Beam Deflection via the Integral Rohit Transform

This paper establishes an elegant scientific framework for finding the exact solution of the space-fractional Euler Bernoulli beam equation by applying the integral Rohit Transform (IRT). The governing fractional differential equation of order 4𝛼, which is based on the Caputo derivative, is transformed into an algebraic equation in the transform domain. Solutions in closed form are derived for a loading distribution that is uniform, and the classical beam solution is obtained as a special case when 𝛼 = 1. Graphical results show how the fractional order affects the structural stiffness and the deflection behavior of the structure. The method constitutes an analytical framework that is not only general but also seamlessly links classical and nonlocal fractional beam theories.