On Abundant New Solutions of Two Fractional Complex Models
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Date
2020
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Springer
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GOLD
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Abstract
We use an analytical scheme to construct distinct novel solutions of two well-known fractional complex models (the fractional Korteweg-de Vries equation (KdV) equation and the fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation). A new fractional definition is used to covert the fractional formula of these equations into integer-order ordinary differential equations. We obtain solitons, rational functions, the trigonometric functions, the hyperbolic functions, and many other explicit wave solutions. We illustrate physical explanations of these solutions by different types of sketches.
Description
M. A. Khater, Mostafa/0000-0001-8466-168X
ORCID
Keywords
Fractional Korteweg-De Vries (Kdv) Equation, Fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (Zkbbm) Equation, Abr Fractional Operator, Modified Khater (Mk) Method, Fractional Zakharov–Kuznetsov–Benjamin–Bona–Mahony (ZKBBM) equation, Economics, Periodic Wave Solutions, Mathematical analysis, Quantum mechanics, Fractional Korteweg–de Vries (KdV) equation, Differential equation, Discrete Solitons in Nonlinear Photonic Systems, QA1-939, FOS: Mathematics, Anomalous Diffusion Modeling and Analysis, Order (exchange), Korteweg–de Vries equation, Physics, Fractional calculus, Rational function, Pure mathematics, ABR $\mathcal{ABR}$ fractional operator, Statistical and Nonlinear Physics, Partial differential equation, Modified Khater (mK) method, Applied mathematics, Fractional Derivatives, Physics and Astronomy, Modeling and Simulation, Physical Sciences, Nonlinear system, Trigonometry, Mathematics, Ordinary differential equation, Finance, Rogue Waves in Nonlinear Systems, Fractional derivatives and integrals, Soliton solutions, \(\mathcal{ABR}\) fractional operator, Fractional partial differential equations, fractional Korteweg-de Vries (KdV) equation, modified Khater (mK) method, Rossby waves, KdV equations (Korteweg-de Vries equations), fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation
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Fields of Science
01 natural sciences, 0103 physical sciences
Citation
Khater, Mostafa M. A...at all 820209. "On abundant new solutions of two fractional complex models", Advances in Difference Equations, Vol. 2020, No. 1.
WoS Q
Q1
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OpenCitations Citation Count
23
Source
Advances in Difference Equations
Volume
2020
Issue
1
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CrossRef : 12
Scopus : 34
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34
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42
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1
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