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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Computational Solutions of some Nonlinear Transportation Equations of Fractional Order via Two Efficient Methods

Discontinuity, Nonlinearity, and Complexity 12(1) (2023) 111--125 | DOI:10.5890/DNC.2023.03.009

Muhammad Abaid Ur Rehman$^1$, Jamshad Ahmad$^1$, Qazi Mahmood Ul Hassan$^2$

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The fundamental objective of this paper is to tackle the time-fractional order transportation equations through two analytical methods, the method of q-homotopy analysis (q-HAM) and the method of reduced differential transform (RDTM) through numerical computation and simulations. The fractional derivative is considered in Caputo's sense. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed methods for theoretical and numerical analysis purpose. The techniques provide series-form solution that converges sharply to the exact solution as the non-integer order approaches the integer order. Also, the graphical depictions of solutions are provided to compare the results of these methods.


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