A new numerical technique for solving Caputo time-fractional biological population equation

Khalouta, Ali; Kadem, Abdelouahab

doi:10.3934/math.2019.5.1307

Cited by 13 publications

(13 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Obeidat and Bentil in [19,20] have developed new technique called the tempered fractional natural transform method (TFNTM) where they presented new theories and they proved the existence and uniqueness theorems of the TFNTM and they implemented the method to solve some tempered fractional ODEs and PDEs. Our remit to solve a degenerate parabolic equation arising in the spatial diffusion of biological populations of fractional order with given initial conditions [21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models

Obeidat

Bentil

2022

Numerical Methods Partial

View full text Add to dashboard Cite

In this study, we present convergence analysis along with an error estimate for time-fractional biological population equation in terms of the Caputo derivative using a new technique called the fractional decomposition method (FDM). Further, we present exact solutions to four test problems of nonlinear time-fractional biological population models to show the accuracy and efficiency of the FDM. This method based on constructing series solutions in a form of rapidly convergent series with easily computable components and without the need of linearization, discretization and perturbations. The results prove that the FDM is very effective and simple for solving fractional partial differential equations in multi-dimensional spaces, special cases of which we have described in this paper.

show abstract

Section: Introductionmentioning

confidence: 99%

Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models

Obeidat

Bentil

2022

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

“…Numerous mathematical procedures have been presented to get results of NLCMs, for example, homotopy perturbation method [1], residual power series method [2], Shifted Jacobi spectral collocation method [3], reproducing kernel Hilbert space method [4], modified generalized Taylor fractional series method [5], the improved fractional Riccati extension scheme [6], method of separation variables [7], generalized ðG′/GÞ -extension scheme [8], Chebyshev collocation way [9], rational ðG′/GÞ-extension scheme [10], the first integral way [11], modified exp-task way [12], variational iteration method [13], modified Khater method [14], and iterative reproducing kernel Hilbert space approach [15].…”

Section: Introductionmentioning

confidence: 99%

New Results of Some of the Conformable Models Arising in Dynamical Systems

Alam

İlhan

Manafian

et al. 2022

Advances in Mathematical Physics

View full text Add to dashboard Cite

This article investigates the new results of three nonlinear conformable models (NLCMs). To study such varieties of new soliton structures, we perform the generalized Kudryashov (GK) method. The obtained new results are defined in the styles of the exponential and rational functions. The derived new soliton structures are stable, serviceable, and fitting to embrace the conformable dynamics, chaotic vibrations, global bifurcations, optimal control problems, fluid mechanics, plasma physics, system identification, local bifurcations, control theory and resonances, and so many. The outcomes declare that the process is hugely valuable and accessible for investigating nonlinear conformable order models treated in theoretical physics.

show abstract

“…Many other researchers have applied NIM and natural transform for handling the FDEs [14][15][16][17]. In this article, we will consider fractional biological population model (FBPM) as [18]…”

Section: Introductionmentioning

confidence: 99%

Analytical Approximate Solution of the Fractional Order Biological Population Model by Using Natural Transform

Ali

Nawaz

Zada

et al. 2022

Journal of Nanomaterials

View full text Add to dashboard Cite

In the present work, the natural transform iterative method (NTIM) is implemented to solve the biological population model (BPM) of fractional order. The method is tested for three nonlinear examples. The NTIM is a combination of a new iterative method and natural transform. We see that the solution pattern converges to the exact solution in a few iterations. The method handles an extensive range of differential equations of both fractional and integer order. The fractional order derivative is considered in Caputo’s sense. For mathematical computation, Mathematica 10 is used.

show abstract

A new numerical technique for solving Caputo time-fractional biological population equation

Cited by 13 publications

References 10 publications

Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models

Convergence analysis of the fractional decomposition method with applications to time‐fractional biological population models

New Results of Some of the Conformable Models Arising in Dynamical Systems

Analytical Approximate Solution of the Fractional Order Biological Population Model by Using Natural Transform

Contact Info

Product

Resources

About