Application of fractional-order Fibonacci wavelets to solve variable-order fractional partial differential equations

چکیده مقاله

In this chapter, we solve a widely used model of variable-order fractional partial differential equations consisting of linear and nonlinear terms. We develop a novel computational method based on fractional-order Fibonacci wavelets and the least square approximation method. To do this, first, we construct fractional-order Fibonacci wavelets. Then we propose a variable-order Riemann–Liouville pseudo-operational matrix and an extra fractional-order Riemann–Liouville pseudo-operational matrix for these functions to design the method. These matrices and the least square approximation method are used to convert the considered equation to a system of algebraic equations. The properties of pseudo-operational matrices have reflected well in the process of the suggested scheme and have created a numerical solution with high precision. Finally, we compare the results with the outcomes of some existing techniques to show the effectiveness and accuracy of the present method. © 2024 Elsevier Inc. All rights are reserved including those for text and data mining AI training and similar technologies.