ON THE HIGHER-ORDER Λ-FRACTIONAL BENDING BEAM

Alireza Khabiri, Reza Taghipour, Ali Asgari and Hossein Jafari
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Alireza Khabiri: Department of Civil Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar 47416-13534, Iran
Reza Taghipour: Department of Civil Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar 47416-13534, Iran
Ali Asgari: Department of Civil Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar 47416-13534, Iran
Hossein Jafari: ��Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences (SIMATS), Chennai 602105, Tamil Nadu, India‡Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran§Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa¶Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110122, Taiwan

FRACTALS (fractals), 2025, vol. 33, issue 09, 1-10

Abstract: This work extends the Λ-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 Λ-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 Λ-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.

Keywords: Fractional Bending Beams; Fractional Curve Space; Λ-Fractional; Spatial Fractional Euler–Bernoulli Beam (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500896

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