Numerical solution of the nonlinear conformable space–time fractional partial differential equations

In this paper, a numerical approach for solving the nonlinear space-time fractional partial differential equations with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second...

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Bibliographic Details
Published inIndian journal of pure and applied mathematics Vol. 52; no. 2; pp. 407 - 419
Main Author Yaslan, H. Çerdik
Format Journal Article
LanguageEnglish
Published New Delhi Indian National Science Academy 01.06.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Chebyshev approximation
Finite difference method
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Research
Partial differential equations
Polynomials
Shifted Chebyshev polynomials of the second kind
35G31
65M70
Conformable fractional derivative
Nonlinear space–time fractional partial differential equation
35R11
Newton method
Finite difference method
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Summary:In this paper, a numerical approach for solving the nonlinear space-time fractional partial differential equations with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind and finite difference method. The proposed scheme reduces the main problem to a system of nonlinear algebraic equations. The validity and the applicability of the proposed technique are shown by numerical examples.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-021-00057-0