New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations

Journal Article · Sat Sep 15 04:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-018-0627-1· OSTI ID:22769207

Baleanu, Dumitru ^[1]; Atangana, Abdon ^[2]

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1. Cankaya University, Department of Mathematics, Faculty of Sciences (Turkey)
2. University of the Free State, Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences (South Africa)

In this paper, we extend the model of the Korteweg–de Vries (KDV) and Korteweg–de Vries–Burger’s (KDVB) to new model time fractional Korteweg–de Vries (TFKDV) and time fractional Korteweg–de Vries-Burger’s (TFKDVB) with Liouville–Caputo (LC), Caputo–Fabrizio (CF), and Atangana-Baleanu (AB) fractional time derivative equations, respectively. We utilize the q-homotopy analysis transform method (q-HATM) to compute the approximate solutions of TFKDV and TFKDVB using LC, CF and AB in Liouville–Caputo sense. We study the convergence analysis of q-HATM by computing the Residual Error Function (REF) and finding the interval of the convergence through the h-curves. Also, we find the optimal values of h so that, we assure the convergence of the approximate solutions. The results are very effective and accurate in solving the TFKDV and TFKDVB.

• OSTI ID: 22769207
• Journal Information: Computational and Applied Mathematics, Journal Name: Computational and Applied Mathematics Journal Issue: 4 Vol. 37; ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
APPROXIMATIONS
CONVERGENCE
EQUATIONS
ERRORS
FUNCTIONS
MATHEMATICAL SOLUTIONS