Based on the fractional black hole entropy (Jalalzadeh S. et al., Eur. Phys. J. C, 81 (2021) 632), we derive modified Friedmann equations from two different frameworks. First, consider modifications of first law thermodynamics at apparent horizon. We show that generalized second (GSL) always holds in a region bounded by Then, obtain Verlinde's entropic gravity framework. also compute correction...

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

In this work we consider explicit Two-derivative Runge-Kutta methods of a specific type where the function f is evaluated only once at each step. New 7th order are presented with minimized dispersion and dissipation error. These two constant coefficients 5 6 stages. Also, modified phase-fitted, amplification-fitted method frequency dependent stages constructed based on Chan Tsai. The new applie...

In this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with ...