Exact Solutions, Lie Symmetry Analysis and Conservation Laws of the Time Fractional Diffusion-Absorption Equation

Hashemi, Mir Sajjad; Balmeh, Z.; Băleanu, Dumitru

doi:10.1007/978-3-319-91065-9_4

Cited by 5 publications

(3 citation statements)

References 22 publications

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“…where I a is the rate at which mass of the species 0 a 0 produced per unit volume during the chemical reaction in the system. From the Eulerian point of view, above equation is the equation of continuity (or equation of mass conservation) [21].…”

Section: Mass Conservation Of Speciesmentioning

confidence: 99%

Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

et al. 2020

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In the present article, an efficient operational matrix based on the famous Laguerre polynomials is applied for the numerical solution of two-dimensional non-linear time fractional order reaction–diffusion equation. An operational matrix is constructed for fractional order differentiation and this operational matrix converts our proposed model into a system of non-linear algebraic equations through collocation which can be solved by using the Newton Iteration method. Assuming the surface layers are thermodynamically variant under some specified conditions, many insights and properties are deduced e.g., nonlocal diffusion equations and mass conservation of the binary species which are relevant to many engineering and physical problems. The salient features of present manuscript are finding the convergence analysis of the proposed scheme and also the validation and the exhibitions of effectiveness of the method using the order of convergence through the error analysis between the numerical solutions applying the proposed method and the analytical results for two existing problems. The prominent feature of the present article is the graphical presentations of the effect of reaction term on the behavior of solute profile of the considered model for different particular cases.

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Section: Mass Conservation Of Speciesmentioning

confidence: 99%

Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

et al. 2020

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“…Fractional order differential and integral operators, which are nonlocal in nature have various applications in applied branches such as blood flow problems, anomalous diffusion, spreading of disease, control processes, population dynamics, etc. for instance see [1][2][3][4][5][6][7][8][9].…”

Section: Introduction and The Problem Formulationmentioning

confidence: 99%

On the existence and uniqueness of the solution of a nonlinear fractional differential equation with integral boundary condition

Shivanian

2024

Preprint

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This work studies the existence and the uniqueness of the solution to a kind of high-order nonlinear fractional differential equations involving Rieman-Liouville fractional derivative. The boundary condition is of integral type which entangles both starting and ending points of the domain. First, the unique exact solution is extracted in terms of Green’s function for the linear fractional differential equation and then Banach contraction mapping theorem is applied to prove the main result in the case of general nonlinear source term. Furthermore, our main result is demonstrated by an illustrative example to show its legitimacy and applicability.

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“…Analytical methods for solving partial differential equations (PDEs) constitute a rich and diverse toolkit employed across various scientific and engineering disciplines. These analytical methods form the cornerstone of theoretical investigations and are essential for understanding the fundamental behavior of systems described by PDEs [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

Samir,

El-Sham,

El-barkoki

et al. 2024

Contemp. Math.

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The presented research investigates the (2+1)-dimensional perturbed nonlinear Schrödinger model. This model takes into account various effects such as fourth order dispersion, intermodal dispersion, nonlinear dispersion, group velocity dispersion, Kerr nonlinearity and self steepening effects. This model simulates the estimation of optical solitons and a variety of broadcasting networks’ transmission in nonlinear fiber optics. The proposed model is studied using the improved modified extended tanh function technique. For the proposed model, several solitons and other solutions are generated. These solutions including {bright, dark and singular} solitons, singular periodic and Jacobi elliptic solutions. By introducing the two- and three-dimensional graphs, the physical behavior of the retrieved solutions is displayed.

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Exact Solutions, Lie Symmetry Analysis and Conservation Laws of the Time Fractional Diffusion-Absorption Equation

Cited by 5 publications

References 22 publications

Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

On the existence and uniqueness of the solution of a nonlinear fractional differential equation with integral boundary condition

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

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