Time-fractional partial differential equations: a novel technique for analytical and numerical solutions

Yadav, Lokesh Kumar; Agarwal, Garima; Suthar, D. L.; Kumar, Dinesh

doi:10.1080/25765299.2022.2064075

Cited by 12 publications

(3 citation statements)

References 28 publications

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“…erefore, it is extremely important to nd an e ective method of solving fractional di erential equations, as only the solutions can give a better comprehension of the underlying problems. Many researchers have presented di erent methods for solving fractional di erential equations such as reproducing kernel discretization method [10], Chebyshev wavelet collocation method, [11] Tichonov regularization method [12], Chebyshev collocation method, [13] q-homotopy analysis Shehu transform method [14], Fractional di erential transform, [15] Fractional variational iterational method [16], and iterative Laplace transform method [17].…”

Section: Introductionmentioning

confidence: 99%

Solution of Space‐Time Fractional Differential Equations Using Aboodh Transform Iterative Method

Awuya

Ojo²,

Mahmudov

2022

Journal of Mathematics

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A relatively new and efficient approach based on a new iterative method and the Aboodh transform called the Aboodh transform iterative method is proposed to solve space-time fractional differential equations, the fractional order is considered in the Caputo sense. This method is a combination of the Aboodh transform and the new iterative method and gives the solution in series form with easily computable components. The nonlinear term is easily handled by the new iterative method, to affirm the simplicity and performance of the proposed method, five examples were considered, and the solution plots were presented to show the effect of the fractional order. The outcome reveals that the approach is accurate and easy to implement.

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Section: Introductionmentioning

confidence: 99%

Solution of Space‐Time Fractional Differential Equations Using Aboodh Transform Iterative Method

Awuya

Ojo²,

Mahmudov

2022

Journal of Mathematics

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“…The historical and nonlocal distributed effects are considered via fractional differential coefficients; an outstanding literature on this topic may be found in numerous monographs [12][13][14][15]. For this reason, many authors are attracted to knowing the properties of fractional differential equations and vast applications in modeling and engineering fields [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods

Aljahdaly

Shah

Naeem

et al. 2022

Journal of Function Spaces

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The approximate solutions of the time fractional advection-dispersion equation are presented in this article. The nonlocal nature of solute movement and the nonuniformity of fluid flow velocity in the advection-dispersion process lead to the formation of a heterogeneous system, which can be modeled using a fractional advection-dispersion equation, which generalizes the classical advection-dispersion equation and replaces the time derivative with the fractional Caputo derivative. Researchers use a variety of numerical techniques to study such fractional models, but the nonlocality of the derivative having fractional order leads to high computation complexity and complex calculations, so the task is to find an efficient technique that requires less computation and provides greater accuracy when numerically solving such models. A innovative techniques, homotopy perturbation method and new iteration method, are used in connection with the Elzaki transform to solve the “fractional advection-dispersion equation” which provides the solution in the convergent series form. When the homotopy perturbation method is used with the Elzaki transform, fast convergent series solutions can be obtained with less computation. By solving some cases of time-fractional advection-dispersion equation with varied initial conditions with the help of new iterative transform method and homotopy perturbation transform method demonstrates the usefulness of the proposed methods.

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“…Due to the remoteness of some ethnic areas, there are many unexploited natural tourism resources. Reasonable development of local unique natural tourism resources and reasonable publicity can promote the development of local tourism [4].…”

Section: Introductionmentioning

confidence: 99%

The Development of Tourism Towns with Characteristic Ancient Buildings Based on Partial Differential Model of Competitive Resource Optimization

Jiang

2022

Mathematical Problems in Engineering

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In this paper, a deep learning-based method for solving high-dimensional nonlinear partial differential equations is proposed, that is, the deep backward stochastic differential equation method. The solution function of the high-dimensional partial differential equation is represented by the corresponding solution function of the backward stochastic differential equation. The substantive carrier of ancient town tourism is the ancient town itself. The essence of resources and the ancient town are highly unified, resource occupiers (suppliers) and tourism participants are highly unified, and tourists need to be highly coupled with the essence of tourism products. The art of ancient architecture is not only an important material basis for the sustainable development of the local tourism industry but also an important experience reference for the traditional architectural design of the creation of artistic architecture in the new era. To create a tourist destination of ancient architecture in a characteristic town, it will contribute to the sustainable development of the local economy and society. Taking the policy support related to tourism of ancient buildings as the starting point, and the internal cultural heritage as the basis for development, we explore the characteristic activities and products, integrate natural tourism resources and modern tourism resources in the whole region, to help ancient buildings become an important driving force to promote the development of the tourism industry.

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Time-fractional partial differential equations: a novel technique for analytical and numerical solutions

Cited by 12 publications

References 28 publications

Solution of Space‐Time Fractional Differential Equations Using Aboodh Transform Iterative Method

Solution of Space‐Time Fractional Differential Equations Using Aboodh Transform Iterative Method

A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods

The Development of Tourism Towns with Characteristic Ancient Buildings Based on Partial Differential Model of Competitive Resource Optimization

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