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The analysis of Oldroyd fluids; a class of Maxwell fluids which also bears Newtonian properties under some conditions, has important implications for different scientific and engineering/industrial applications. Examples of these fluids are typically dilute polymer solutions which demonstrate both viscous and elastic behaviors when subjected to strain. For unidirectional steady flows, the Oldroyd-B (3-Constant) model is the simplest when it comes to describing these behaviors. This model is not sufficient in certain cases, for instance, convergent flow channels, pulling effects, and other extensional flows. In all such scenarios, its application may lead to having out of bound tensile stresses. Hence, in all practicality, higher constants of the Oldroyd model are required to include different tensorial invariants. In this article, we perform this analysis in fractional space on Oldroyd fluids in thin-film flow context using the Oldroyd 6-Constant model for both lifting and drainage scenarios. Solutions to the highly non-linear fractional differential equations are obtained by means of the Homotopy Perturbation Method (HPM) along with fractional calculus. Validation and convergence of the solutions are confirmed by finding residual errors. To the best of our knowledge, the given problem has not been attempted before in fractional space. Various physical aspects, such as the velocity profile, volumetric flux and average velocities are determined and analyzed both graphically and in tabulation form as part of this analysis. [ABSTRACT FROM AUTHOR]

Under a microgravity condition, the microgravity-induced motion of a rigid pendulum has many special properties, which cannot be successfully revealed by any known theory. This work suggests a new fractal model for this purpose to describe the microgravity-induced motion by using the fractal derivative, and its variational principle is successfully established according to the semi-inverse method. The variational principle is very helpful to construct conservation laws and to suggest solution structures of the new fractal model. The approximate analytical solution of the model is gained by the two-scale transform method and the homotopy perturbation method. [ABSTRACT FROM AUTHOR]

A fractal modification of the telegraph equation with fractal derivatives is given, and its variational principle is established by the semi-inverse method. The two-scale transform method and He's homotopy perturbation method are successfully adopted to solve the fractal equation. [ABSTRACT FROM AUTHOR]

In this paper, a fractional Zakharov-Kuznetsov equation with He's fractional derivative is studied by the fractional complex transform and He's homotopy perturbation method. The solution process is elucidated step by step to show its simplicity and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this work, we apply three different techniques to solve the Fitzhugh–Nagumo equation that is an important equation used to describe the propagation of electrical signals in excitable media, such as nerve fibers. Residual power series method (RPSM), homotopy perturbation method (HPM), and a modified fractional Taylor expansion, are applied to this nonlinear equation to obtain approximate solutions. By comparing the exact solution with the approximate solutions obtained from the methods suggested we demonstrate that these methods are efficient tools to solve nonlinear fractional partial differential equations (NFPDE) this is due to the high accuracy obtained. To support the current solution investigation, various graphs in 2D and 3D are shown. • Three different techniques are applied to solve the Fitzhugh–Nagumo equation. • By comparing the exact solution with the approximate solutions obtained from the methods. • To support the current solution investigation, various graphs in 2D and 3D are shown. [ABSTRACT FROM AUTHOR]