In this article, we consider cancer tumor models and investigate the need for fractional order derivative as compared to classical first in time. Three different cases of net killing rate are taken into account including case where cells is dependent on concentration cells. At first, use a relatively new analytical technique called q-Homotopy Analysis Method resulting time-fractional partial differential equations obtain solution form convergent series with easily computable components. Our...

In this present investigation, we proposed a reliable and new algorithm for solving time‐fractional differential models arising from physics engineering. This employs the Shehu transform method, then nonlinearity term is decomposed. We apply to solve many of practical importance outcomes show that method efficient, precise, easy use. Closed form solutions are obtained in cases, exact some special cases. Furthermore, solution profiles presented behavior results other better understand effect...

Abstract In this paper, we present analytical-approximate solution to the time-fractional nonlinear coupled Jaulent–Miodek system of equations which comes with an energy-dependent Schrödinger potential by means a residual power series method (RSPM) and q-homotopy analysis (q-HAM). These methods produce convergent solutions easily computable components. Using specific example, comparison is done between these exact solution. The numerical results show that are competitive, powerful, reliable,...

This paper presents analytical-approximate solutions of the time-fractional Cahn-Hilliard (TFCH) equations fourth and sixth order using new iterative method (NIM) q-homotopy analysis (q-HAM). We obtained convergent series these two methods. The simplicity accuracy methods in solving strongly nonlinear fractional differential is displayed through examples provided. In case where exact solution exists, error estimates are also investigated.

Abstract This paper employs an efficient technique, namely q-homotopy analysis transform method, to study a nonlinear coupled system of equations with Caputo fractional-time derivative. The fractional systems studied in this present investigation are the generalized Hirota–Satsuma KdV, and modified KdV which used as model physical phenomena arising biology, chemistry, physics, engineering. series solution obtained using method is proved be reliable accurate minimal computations. Several...

The novel coronavirus (SARS-CoV-2), or COVID-19, has emerged and spread at fast speed globally; the disease become an unprecedented threat to public health worldwide. It is one of greatest challenges in modern times, with no proven cure vaccine. In this paper, our focus on a fractional order approach modeling simulations COVID-19. We introduce type susceptible-exposed-infected-recovered (SEIR) model gain insight into ongoing pandemic. Our proposed incorporates transmission rate, testing...

In this study, we consider conformable type Coudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation. Three powerful analytical methods are employed to obtain generalized solutions of the nonlinear equation interest. First, sub-equation method is used as baseline where closed form obtained and exact for any fractional order [Formula: see text]. Furthermore, residual power series (RPSM) text]-homotopy analysis ([Formula: text]-HAM) then applied approximate solutions. These possible using some...

In this paper, we introduce and study a new class of split inverse problems, named hierarchical monotone variational inclusion problem with multiple output sets in real Hilbert spaces. By using the inertial technique self-adaptive step size strategy, propose analyze Mann-type iterative method for solving problem. The convergence analysis proposed under some suitable conditions is studied. Also, show that sequence iterates generated by converges strongly to minimum-norm solution As...

We consider non-linear homogeneous and non-homogeneous gas dynamic equations of time-fractional type in this paper.The approximate solutions these are calculated the form series obtained by q-Homotopy Analysis Method (q-HAM).Exact solution is for timefractional case while non-homogeneous, exact possible special case.This due to ability control auxiliary parameter h fraction factor present method.The presence fraction-factor method gives it an edge over other existing analytical methods...