An operational matrix method for solving variable-order fractional biharmonic equation

作者：Heydari, M. H.; Avazzadeh, Z.^*

来源：COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37(4): 4397-4411.

DOI：10.1007/s40314-018-0580-z

• Variable-order fractional biharmonic equation (V-OFBE)
• Shifted second kind Chebyshev polynomials
• Operational matrix method
• Operational matrix of variable-order fractional derivative

In this paper, we focus on the fourth-order biharmonic equation which also has been appeared with fractional derivative order. Then, we generalize the fractional biharmonic equation using the concept of variable-order (V-O) fractional derivative in the type of Caputo namely V-O fractional biharmonic equation (V-OFBE). To establish a method for solving V-OFBE, we firstly derive the operational matrix of V-O fractional derivatives for the shifted second kind Chebyshev polynomials. For obtaining this operational matrix with a general procedure, we implement the analytical form of these polynomials and some properties of the V-O fractional derivatives. This approach reduces the V-OFBE to a system of algebraic equations which considerably decreases the following computations. The applicability and reliability of the proposed method are investigated by solving some test problems. The experimental results show the spectral rate of convergence.

• 出版日期2018-9
• 单位南京师范大学