Novel Numerical Approach for Time Fractional Equations with Nonlocal Condition

Deswal, Komal; Kumar, Devendra; Băleanu, Dumitru

doi:10.1007/s11075-023-01614-w

Cited by 3 publications

(1 citation statement)

References 24 publications

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“…Combining the Riemann-Liouville integral and Caputo derivative, the CPC operator is a trustworthy, efficient, and versatile operator. New research on the fractional-order mathematical representations under the CPC operator of some other viral diseases can be found in [23][24][25][26]. The Laplace-Adomian decomposition methodology solves stochastic and deterministic differential equations more effectively than traditional techniques by converting differential equations into their algebraic equivalents and decomposing nonlinear elements into Adomain polynomials [27,28].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Transmission and Mathematical Analysis of Ebola Virus Using a Constant Proportional Operator with a Power Law Kernel

Xu,

Farman

2023

Fractal Fract

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The Ebola virus continues to be the world’s biggest cause of mortality, especially in developing countries, despite the availability of safe and effective immunization. In this paper, we construct a fractional-order Ebola virus model to check the dynamical transmission of the disease as it is impacted by immunization, learning, prompt identification, sanitation regulations, isolation, and mobility limitations with a constant proportional Caputo (CPC) operator. The existence and uniqueness of the proposed model’s solutions are discussed using the results of fixed-point theory. The stability results for the fractional model are presented using Ulam–Hyers stability principles. This paper assesses the hybrid fractional operator by applying methods to invert proportional Caputo operators, calculate CPC eigenfunctions, and simulate fractional differential equations computationally. The Laplace–Adomian decomposition method is used to simulate a set of fractional differential equations. A sustainable and unique approach is applied to build numerical and analytic solutions to the model that closely satisfy the theoretical approach to the problem. The tools in this model appear to be fairly powerful, capable of generating the theoretical conditions predicted by the Ebola virus model. The analysis-based research given here will aid future analysis and the development of a control strategy to counteract the impact of the Ebola virus in a community.

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Section: Introductionmentioning

confidence: 99%

Dynamical Transmission and Mathematical Analysis of Ebola Virus Using a Constant Proportional Operator with a Power Law Kernel

Xu,

Farman

2023

Fractal Fract

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A Numerical Simulation of Chemical Contaminant Transport Problems in Inhomogeneous Media Using a 2d-Tfdcr Model

Azis

2024

Preprint

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A Two-Dimensional Nonlocal Fractional Parabolic Initial Boundary Value Problem

Mesloub,

Alhazzani,

Gadain

2024

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In this paper, we investigate a two-dimensional singular fractional-order parabolic partial differential equation in the Caputo sense. The partial differential equation is supplemented with Dirichlet and weighted integral boundary conditions. By employing a functional analysis method based on operator theory techniques, we prove the existence and uniqueness of the solution to the posed nonlocal initial boundary value problem. More precisely, we establish an a priori bound for the solution from which we deduce the uniqueness of the solution. For proof of its existence, we use various density arguments.

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Novel Numerical Approach for Time Fractional Equations with Nonlocal Condition

Cited by 3 publications

References 24 publications

Dynamical Transmission and Mathematical Analysis of Ebola Virus Using a Constant Proportional Operator with a Power Law Kernel

Dynamical Transmission and Mathematical Analysis of Ebola Virus Using a Constant Proportional Operator with a Power Law Kernel

A Numerical Simulation of Chemical Contaminant Transport Problems in Inhomogeneous Media Using a 2d-Tfdcr Model

A Two-Dimensional Nonlocal Fractional Parabolic Initial Boundary Value Problem

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