On the Solutions of Non-Linear Time-Fractional Gas Dynamic Equations: An Analytical Approach

Iyiola, Olaniyi S.

doi:10.12732/ijpam.v98i4.8

Cited by 42 publications

(33 citation statements)

References 14 publications

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“…The search for a better way to expand the convergence region led to the modification of HAM, called q-HAM, more of a general method than HAM [48]. Many authors have taken advantage of q-HAM and used it to solve nonlinear fractional partial differential equations [49][50][51][52][53][54][55]. The q-HATM was proposed by Singh et al [56] and did not require any form of discretization, linearization, or perturbation as compared to other methods.…”

Section: Introductionmentioning

confidence: 99%

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

Akinyemi

Iyiola

2020

Adv Differ Equ

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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 nonlinear fractional coupled systems studied in this present investigation are the generalized Hirota-Satsuma coupled with KdV, the coupled KdV, and the modified coupled KdV equations which are used as a model in nonlinear physical phenomena arising in biology, chemistry, physics, and engineering. The series solution obtained using this method is proved to be reliable and accurate with minimal computations. Several numerical comparisons are made with well-known analytical methods and the exact solutions when α = 1. It is evident from the results obtained that the proposed method outperformed other methods in handling the coupled systems considered in this paper. The effect of the fractional order on the problem considered is investigated, and the error estimate when compared with exact solution is presented.Here, we present some useful definitions, properties, and notations that will be used in this work. Definition 2.1 The Riemann-Liouville (R-L) fractional integral of order α (α ≥ 0) of a function Q(x, t) ∈ C m , m ≥ -1, is given as [29, 63-65] J α Q(x, t) = 1 Γ (α) t 0

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Section: Introductionmentioning

confidence: 99%

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

Akinyemi

Iyiola

2020

Adv Differ Equ

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“…Though every model should seek to use fractional calculus when introducing a new model, solving such model is known to be very difficult and required strong numerical or analytical techniques. Some of the methods used in the literature are homotopy perturbation method [17][18][19][20][21], Laplace analysis method [22], homotopy analysis method [23][24][25][26][27], Adomian decomposition method [28], differential transformation method [29], perturbation-iteration algorithm [30], iterative Shehu transform method [31], residual power series method [32][33][34][35][36][37][38][39][40] and q-homotopy analysis transform method in [41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

A fractional order approach to modeling and simulations of the novel COVID-19

Owusu‐Mensah

Akinyemi

Oduro

et al. 2020

Preprint

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The novel coronavirus (SARS-CoV-2.) has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public health challenges in modern times, with no proven cure or vaccine. In this paper, our focus is on a fractional order approach to modeling and simulations of the novel COVID-19. We introduce a fractional type Susceptible-Exposed-Infected-Recovered (SEIR) model to gain insight into the ongoing pandemic of COVID-19. Our proposed model incorporates transmission rate, testing rates, and transition rate (from asymptomatic to symptomatic population groups) for a holistic study of the coronavirus disease. The impacts of these parameters on the dynamics of the solution proles for the disease are simulated and discussed in detail. Furthermore, across all the different parameters, the effects of the fractional order derivative are also simulated and discussed in detail. Various simulations carried out enable us gain deep insights into the dynamics of the spread of COVID-19. The simulation results confirm that fractional calculus is an appropriate tool in modeling the spread of a complex infectious disease such as the novel COVID-19. In the absence of vaccine and treatment, our analysis strongly supports the significance reduction in the transmission rate as valuable strategy to curb the spread of the virus. Our results suggest that tracing and moving testing up has an important benefit. It reduces the number of infected individuals in the general public and thereby reduce the spread of the pandemic. Once the infected individuals are identified and isolated, the interaction between susceptible and infected individuals diminishes and transmission reduces. Furthermore, aggressive testing is also highly recommended.

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“…There are several methods used in obtaining approximate solutions to linear and nonlinear FPDE such as the Adomian decomposition method (ADM) [28,29], the homotopyperturbation method (HPM) [30][31][32][33][34], the variational iteration method (VIM) [35], the q-homotopy analysis transform method (q-HATM) [36,37], the fractional natural decomposition method (FNDM) [38], the fractional multi-step differential transformed method (FMsDTM) [39], the new iterartive method (NIM) [40][41][42] and the homotopy analysis method (HAM) [43][44][45][46]. In a recent development, [47][48][49][50][51][52][53], a modified homotopy analysis method was established which has potential applications in a wide range of systems of differential equations. This method provides a convenient way to ascertain the convergence of approximation series and even exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Efficient analytical techniques for solving time-fractional nonlinear coupled Jaulent–Miodek system with energy-dependent Schrödinger potential

et al. 2019

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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 of a residual power series method (RSPM) and a q-homotopy analysis method (q-HAM). These methods produce convergent series solutions with easily computable components. Using a specific example, a comparison analysis is done between these methods and the exact solution. The numerical results show that present methods are competitive, powerful, reliable, and easy to implement for strongly nonlinear fractional differential equations.

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On the Solutions of Non-Linear Time-Fractional Gas Dynamic Equations: An Analytical Approach

Cited by 42 publications

References 14 publications

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

A fractional order approach to modeling and simulations of the novel COVID-19

Efficient analytical techniques for solving time-fractional nonlinear coupled Jaulent–Miodek system with energy-dependent Schrödinger potential

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