New numerical approach for time-fractional partial differential equations arising in physical system involving natural decomposition method

Rashid, Saima; Kubra, Khadija Tul; Rauf, Asia; Chu, Yu‐Ming; Hamed, Y. S.

doi:10.1088/1402-4896/ac0bce

Cited by 15 publications

(8 citation statements)

References 41 publications

(46 reference statements)

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“…Numerous researchers have proposed several schemes to solve the time-fractional KdV equation using different methods, such as the Adomian decomposition method (ADM) [9], differential transform method (DTM) [10], homotopy analysis method (HAM) [11], Natural decomposition method (NDM) [12], variational iteration method [13], Elzaki projected differential transform method (EPDTM) [14], modified tanh technique (MTT) [15], new iterative method (NIM) [16], Lie symmetry analysis (LSA) [17], spectral volume method (SVM) [18,19] and so on. Analogously, similar results for (2) have been proposed by Fan [20], Cavlak and Inc [21], Inc et al [22], Lin et al [23], Karczewska and Szczeciński [24] and Ghoreishi et al [25].…”

Section: Introductionmentioning

confidence: 99%

A Novel Analytical View of Time-Fractional Korteweg-De Vries Equations via a New Integral Transform

et al. 2021

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We put into practice relatively new analytical techniques, the Shehu decomposition method and the Shehu iterative transform method, for solving the nonlinear fractional coupled Korteweg-de Vries (KdV) equation. The KdV equation has been developed to represent a broad spectrum of physics behaviors of the evolution and association of nonlinear waves. Approximate-analytical solutions are presented in the form of a series with simple and straightforward components, and some aspects show an appropriate dependence on the values of the fractional-order derivatives that are, in a certain sense, symmetric. The fractional derivative is proposed in the Caputo sense. The uniqueness and convergence analysis is carried out. To comprehend the analytical procedure of both methods, three test examples are provided for the analytical results of the time-fractional KdV equation. Additionally, the efficiency of the mentioned procedures and the reduction in calculations provide broader applicability. It is also illustrated that the findings of the current methodology are in close harmony with the exact solutions. It is worth mentioning that the proposed methods are powerful and are some of the best procedures to tackle nonlinear fractional PDEs.

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Section: Introductionmentioning

confidence: 99%

A Novel Analytical View of Time-Fractional Korteweg-De Vries Equations via a New Integral Transform

et al. 2021

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“…The development of accurate and explicit solutions to nonlinear PDEs is a challenging task in applied sciences, and it is one of the most promising and productive research areas. Due to these facts, numerous mathematical methods for configuring approximate solutions have been proposed, such as the Adomian decomposition method (ADM) [11][12][13], homotopy perturbation method (HPM) [14,15], Laplace iterative transform method (LITM) [16], q-homotopy analysis method (q-HAM) [17], Haar wavelet method (HWM) [18], Lie symmetry analysis (LSA) [19], Chebyshev spectral collocation method (CSCM) [20], and many more.…”

Section: Introductionmentioning

confidence: 99%

Novel Computations of the Time-Fractional Fisher’s Model via Generalized Fractional Integral Operators by Means of the Elzaki Transform

et al. 2021

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The present investigation dealing with a hybrid technique coupled with a new iterative transform method, namely the iterative Elzaki transform method (IETM), is employed to solve the nonlinear fractional Fisher’s model. Fisher’s equation is a precise mathematical result that arose in population dynamics and genetics, specifically in chemistry. The Caputo and Antagana-Baleanu fractional derivatives in the Caputo sense are used to test the intricacies of this mechanism numerically. In order to examine the approximate findings of fractional-order Fisher’s type equations, the IETM solutions are obtained in series representation. Moreover, the stability of the approach was demonstrated using fixed point theory. Several illustrative cases are described that strongly agree with the precise solutions. Moreover, tables and graphs are included in order to conceptualize the influence of the fractional order and on the previous findings. The projected technique illustrates that only a few terms are sufficient for finding an approximate outcome, which is computationally appealing and accurate to analyze. Additionally, the offered procedure is highly robust, explicit, and viable for nonlinear fractional PDEs, but it could be generalized to other complex physical phenomena.

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“…The ADM is a semi-analytical approach to solving linear-nonlinear FDEs by advantageously creating a functional series solution, initially presented by Adomian [48]. Later, this approach was used with numerous transformations (such as the Sumudu, Aboodh, Laplace, and Mohand transforms), as shown in [49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Analytic Fuzzy Formulation of a Time-Fractional Fornberg–Whitham Model with Power and Mittag–Leffler Kernels

et al. 2021

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This manuscript assesses a semi-analytical method in connection with a new hybrid fuzzy integral transform and the Adomian decomposition method via the notion of fuzziness known as the Elzaki Adomian decomposition method (briefly, EADM). Moreover, we use the aforesaid strategy to address the time-fractional Fornberg–Whitham equation (FWE) under gH-differentiability by employing different initial conditions (IC). Several algebraic aspects of the fuzzy Caputo fractional derivative (CFD) and fuzzy Atangana–Baleanu (AB) fractional derivative operator in the Caputo sense, with respect to the Elzaki transform, are presented to validate their utilities. Apart from that, a general algorithm for fuzzy Caputo and AB fractional derivatives in the Caputo sense is proposed. Some illustrative cases are demonstrated to understand the algorithmic approach of FWE. Taking into consideration the uncertainty parameter ζ∈[0,1] and various fractional orders, the convergence and error analysis are reported by graphical representations of FWE that have close harmony with the closed form solutions. It is worth mentioning that the projected approach to fuzziness is to verify the supremacy and reliability of configuring numerical solutions to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

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New numerical approach for time-fractional partial differential equations arising in physical system involving natural decomposition method

Cited by 15 publications

References 41 publications

A Novel Analytical View of Time-Fractional Korteweg-De Vries Equations via a New Integral Transform

A Novel Analytical View of Time-Fractional Korteweg-De Vries Equations via a New Integral Transform

Novel Computations of the Time-Fractional Fisher’s Model via Generalized Fractional Integral Operators by Means of the Elzaki Transform

Analytic Fuzzy Formulation of a Time-Fractional Fornberg–Whitham Model with Power and Mittag–Leffler Kernels

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