Novel Dynamic Structures of 2019-nCoV with Nonlocal Operator via Powerful Computational Technique

Gao, Wei; Veeresha, P.; Prakasha, D. G.; Baskonus, Hacı Mehmet

doi:10.3390/biology9050107

Cited by 135 publications

(85 citation statements)

References 65 publications

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“…For the Kawahara equation, recently Cui et al [63] derived the local well-posedness with−1 < s < 0 when = 0. Moreover, the time-fractional B-L equation is analyzed with various methods including, Variational iteration methods and Homotopy perturbation [60], Residual power series method [64], Reduced differential transform method [61], and others [14,17,24,[65][66][67][68][69][70][71][72].…”

Section: Introductionmentioning

confidence: 99%

New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques

Gao

Veeresha

Prakasha

et al. 2020

Numerical Methods Partial

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The pivotal aim of the present work is to find the numerical solution for fractional Benney-Lin equation by using two efficient methods, called q-homotopy analysis transform method and fractional natural decomposition method. The considered equation exemplifies the long waves on the liquid films. Projected methods are distinct with solution procedure and they are modified with different transform algorithms. To illustrate the reliability and applicability of the considered solution procedures we consider eight special cases with different initial conditions. The fractional operator is considered in Caputo sense. The achieved results are drowned through two and three-dimensional plots for different Brownian motions and classical order. The numerical simulations are presented to ensure the efficiency of considered techniques. The behavior of the obtained results for distinct fractional order is captured in the present framework. The outcomes of the present investigation show that, the considered schemes are efficient and powerful to solve nonlinear differential equations arise in science and technology.

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Section: Introductionmentioning

confidence: 99%

New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques

Gao

Veeresha

Prakasha

et al. 2020

Numerical Methods Partial

Self Cite

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“…Fractional calculus based on differential and difference equations is of considerable importance due to their connection with real-world problems that depend not only on the instant time but also on the previous time, in particular, modeling the phenomena by means of fractals, random walk processes, control theory, signal processing, acoustics, and so on (see [1][2][3][4][5][6][7][8][9][10][11][12]). It has been shown that fractional-order models are much more adequate than integer-order models.…”

Section: Introduction and Prelimnariesmentioning

confidence: 99%

Some new local fractional inequalities associated with generalized $(s,m)$-convex functions and applications

et al. 2020

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Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attractive field of research. The fractal sets are the effective tools to describe the accuracy of the inequalities for convex functions. In this paper, we employ linear fractals R α to investigate the (s, m)-convexity and relate them to derive generalized Hermite-Hadamard (HH) type inequalities and several other associated variants depending on an auxiliary result. Under this novel approach, we aim at establishing an analog with the help of local fractional integration. Meanwhile, we establish generalized Simpson-type inequalities for (s, m)-convex functions. The results in the frame of local fractional showed that among all comparisons, we can only see the correlation between novel strategies and the earlier consequences in generalized s-convex, generalized m-convex, and generalized convex functions. We obtain application in probability density functions and generalized special means to confirm the relevance and computational effectiveness of the considered method. Similar results in this dynamic field can also be widely applied to other types of fractals and explored similarly to what has been done in this paper.

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“…Nonlinear differential (DEs) and integro-differential equations (IDEs) have a great importance in modeling of many phenomena in physics and engineering [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Fractional differential equations involving the Caputo and other fractional derivatives, which are a generalization of classical differential equations, have attracted widespread attention [18][19][20][21][22][23][24][25]. In the last decade or so, several studies have been carried out to develop numerical schemes to deal with fractional integro-differential equations (FIDEs) of both linear and nonlinear type.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

et al. 2020

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In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented. The recommended equation with its linear functional argument produces a general form of delay, proportional delay, and advanced non-linear arbitrary order Fredholm–Volterra integro-differential equations. Spectral collocation method is extended to study this problem as a matrix discretization scheme, where the fractional derivatives are characterized in the Caputo sense. The collocation method transforms the given equation and conditions to an algebraic nonlinear system of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. The introduced operational matrix of derivatives includes arbitrary order derivatives and the operational matrix of ordinary derivative as a special case. To the best of authors’ knowledge, there is no other work discussing this point. Numerical test examples are given, and the achieved results show that the recommended method is very effective and convenient.

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Novel Dynamic Structures of 2019-nCoV with Nonlocal Operator via Powerful Computational Technique

Cited by 135 publications

References 65 publications

New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques

New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques

Some new local fractional inequalities associated with generalized $(s,m)$-convex functions and applications

Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

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