Shalouf, M.M.Shloof, A.M.Hamead, H.A.Senu, N.Ahmadian, A.2026-02-152026-02-1520269783031963100978364203451097835407680299783642364051978303185251097835409597179783031534447978364205440297836423272549783030949099978303200231010.1007/978-3-032-00232-7_442-s2.0-105028297768https://doi.org/10.1007/978-3-032-00232-7_44https://hdl.handle.net/20.500.14517/8804Farees Co. for Technology; Libyan Authority for Exhibitions and Conferences; Lincoln University, Malaysia; The Libyan Academic Attaché in Malaysia; The Libyan Authority for Scientific Research The Libyan Embassy in Kuala Lumpur, MalaysiaIn the past few years, the area of mathematical study has made considerable advances, owing largely to the introduction of artificial intelligence (AI) tools. Among these, artificial neural networks (ANNs) have played an important role in modernizing several mathematical techniques and problem-solving approaches. ANNs have recently become popular as a powerful mathematical research tool, providing an effective alternative to established approaches for solving fractal-fractional differential equations (FFDEs). This paper describes the use of a feed-forward ANN with a hidden layer to address systems resulting from the fractal-fractional Bagley-Torvik differential equation (FFBTDE). In addition, a power series (PS) technique is introduced to increase efficiency. The paper looks at for solving FFBTDE with variable and constant coefficients. The numerical findings show that the suggested strategy not only produces results that closely match exact and reference solutions, but also outperforms existing methods in terms of accuracy. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.eninfo:eu-repo/semantics/closedAccessArtificial Neural NetworksFractal-Fractional Bagley-Torvik Differential EquationFractal-Fractional Caputo DerivativePower SeriesConference Object