Muslih, Sami I.Baleanu, DumitruRabei, EqabSadallah, Madhat2016-08-102025-09-182016-08-102025-09-182011Sadallah, M...et al. (2011). Fractional time action and perturbed gravity. Fractals-Complex Geometry Patterns and Scaling In Nature and Society, 19(2), 243-247. http://dx.doi.org/10.1142/S0218348X110052940218-348X1793-6543https://doi.org/10.1142/S0218348X11005294https://hdl.handle.net/20.500.12416/13480In this paper, we used the scaling concepts of Mandelbrot of fractals in variational problems of mechanical systems in order to re-write the action integral function as an integration over the fractional time. In addition, by applying the variational principle to this new fractional action, we obtained the modified Euler-Lagrange equations of motion in any fractional time of order 0 < alpha <= 1. Two examples are investigated in detail.eninfo:eu-repo/semantics/closedAccessFractional CalculusFractional DerivativesFractional Variational PrincipleArticle10.1142/S0218348X110052942-s2.0-79956223884