The Analysis of Fractional-Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform

Article Mathematics, Applied

Analytical investigation of fractional-order Newell-Whitehead-Segel equations via a novel transform

Mounirah Areshi et al.

Summary: In this paper, two different methods are used to find the solution of the time-fractional Newell-Whitehead-Segel equation, which plays an efficient role in describing stripe patterns in nonlinear systems. The proposed methods provide numerical results that are in strong agreement with an exact solution, and the effectiveness of these methods is demonstrated through graphs and tables. Furthermore, the results show that the solution approaches the exact solution as the fractional order tends towards an integer order. The proposed methods are interesting, easy to use, and highly accurate for solving various nonlinear fractional-order partial differential equations.

AIMS MATHEMATICS (2022)

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Article Mathematics, Applied

On Solutions of Fractional-Order Gas Dynamics Equation by Effective Techniques

Naveed Iqbal et al.

Summary: In this work, the fractional-order gas dynamics equation is calculated using the novel iterative transformation technique and homotopy perturbation transformation technique. The efficacy and validation of the techniques are demonstrated through four examples, showing that the approximate solutions obtained by these methods are accurate and easily applicable to other linear and nonlinear problems.

JOURNAL OF FUNCTION SPACES (2022)

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Article Mathematics, Applied

Controllability of stochastic nonlinear oscillating delay systems driven by the Rosenblatt distribution

T. Sathiyaraj et al.

Summary: This paper investigates the controllability of second-order nonlinear stochastic delay systems driven by Rosenblatt distributions in finite dimensional spaces. The controllability conditions are established using fixed point theory, delayed sine and cosine matrices, and delayed Grammian matrices. The controllability results for these systems are illustrated through numerical simulations.

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS (2021)

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Article Physics, Multidisciplinary

An Analytical Technique, Based on Natural Transform to Solve Fractional-Order Parabolic Equations

Ravi P. Agarwal et al.

Summary: This research article explores the solution of fractional-order parabolic equations using the Adomian decomposition method and natural transform, providing simple and attractive closed form solutions. The obtained results are found to be in good agreement with exact solutions, with convergence observed between fractional and integer-order problem solutions. The technique is considered accurate and can be applied to solve other fractional-order partial differential equations.

ENTROPY (2021)

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Article Physics, Multidisciplinary