(1)Solving a class of boundary value problems and fractional Boussinesq-like equation with β-derivatives by fractional-order exponential trial functions
PDF.pdf
Mohammad Parto-Haghighia, Jalil Manafianb,∗
a Department of Mathematics, University of Bonab, Bonab, Iran
b Department of Applied Mathematics, Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran
Received 3 June 2019; received in revised form 28 November 2019; accepted 28 November 2019
Available online 17 December 2019
Abstract
The nonlinear two-point boundary value problem (TPBVP) is converted to a new form of the problem including integral terms. Then
the combination of weak-form integral equation method (WFIEM) and special functions create a robust and applicable numerical scheme
to solve the problem. To display the accuracy of our method, some examples are investigated. Also, the fractional Boussinesq-like equation
involving the β-derivative has been considered that describes the propagation of small amplitude long capillary-gravity waves on the surface
of shallow water.
© 2019 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Fractional order exponential trial functions; BVPs; Adjoint test functions; Weak-form integral equation method; Two-point boundary value
problem; Fractional Boussinesq-like equation.