A fractional multi-wavelet basis in Banach space and solving fractional delay differential equations

Savadkoohi, Fateme RezaeiRabbani, MohsenAllahviranloo, TofighMalkhalifeh, Mohsen Rostamy2025-04-172025-04-172024Savadkoohi, F. R., Rabbani, M., Allahviranloo, T., & Malkhalifeh, M. R. (2024). A fractional multi-wavelet basis in Banach space and solving fractional delay differential equations. Chaos, Solitons & Fractals, 186, 115313.09600779http://dx.doi.org/10.1016/j.chaos.2024.115313https://hdl.handle.net/20.500.12713/6314In this article, we construct a fractional multi-wavelet basis based on Legendre polynomials to solve fractional delay linear and nonlinear differential equations. For this we introduce an orthonormal fractional basis for Banach space L2[0,1] with suitable inner product which make it effective to decrease computational operations and increase accuracy to find approximate solution of the equations. Also, solving fractional problems by orthogonal basis such as Legendre polynomials has a lower accuracy in comparison with fractional basis. Finally, some examples are solved to show the high accuracy of the presented method, and also to compare with some other works. © 2024eninfo:eu-repo/semantics/closedAccessCaputo Fractional DerivativeFractional Delay Differential EquationsFractional Multi-waveletLegendre PolynomialsRiemann–Liouville İntegralA fractional multi-wavelet basis in Banach space and solving fractional delay differential equationsArticle1862-s2.0-8519934562110.1016/j.chaos.2024.115313Q1