Affiliations: [a] Department of Mathematics, Fasa University, Fasa, Iran. heydari@fasau.ac.ir | [b] The Lab. of Quantum Information Processing, Yazd University, Yazd, Iran. hooshmandasl@yazd.ac.ir | [c] Engineering School (DEIM), University of Tuscia, Viterbo, Italy. cattani@unitus.it | [d] Department of Mathematics, School of Humanities and Sciences, SASTRA University, Tamilnadu, India. hariharan@maths.sastra.edu
Correspondence:
[*]
Address for correspondence: Department of Mathematics, Fasa University, Fasa, Iran
Note: [†] Also affiliated at: Faculty of Mathematics, Yazd University, Yazd, Iran
Abstract: In this paper, a new operational matrix of variable-order fractional derivative (OMV-FD) is derived for the second kind Chebyshev wavelets (SKCWs). Moreover, a new optimization wavelet method based on SKCWs is proposed to solve multi variable-order fractional differential equations (MV-FDEs). In the proposed method, the solution of the problem under consideration is expanded in terms of SKCWs. Then, the residual function and its errors in 2-norm are employed for converting the problem under study to an optimization one, which optimally chooses the unknown coefficients. Finally, the method of constrained extremum is applied, which consists of adjoining the constraint equations obtained from the given initial conditions to the object function obtained from residual function by a set of unknown Lagrange multipliers. The main advantage of this approach is that it reduces such problems to those optimization problems, which greatly simplifies them and also leads to obtain a good approximate solution for them.
Keywords: Second kind Chebyshev wavelets (SKCWs), Optimization method, Operational matrix of variable-order fractional derivative (OMV-FD), Multi variable-order fractional differential equation (MV-FDE), Caputo’s variable-order fractional derivative
