NUMERICAL SOLUTIONS USING AN OPERATIONAL MATRIX FOR NON-SINGULAR KERNEL FRACTIONAL DELAY DIFFERENTIAL EQUATIONS WITH VARIABLE-ORDER
DOI:
https://doi.org/10.31185/bsj.Vol23.Iss47.1643Keywords:
Keywords: Variable-order Spectral method; Fractal differential equations; Nonsingular kernel derivativeAbstract
For solving variable-order fractal-fractional delay equations involving Atangana-Baleanu derivative, an optimum collocation technique using a shifted Legendre operational matrix is suggested. In order to address these problems, we created a new Legendre varying-delay operational matrix, Normalized Legendre polynomial features together with a corresponding Legendre fractional derivative operational matrix are used in this method. This also displays the fractional derivative error bound's Normalized Legendre operational matrix. A collocation approach based on these operational matrices reduces the variable-order fractal-fractional varying-delay differential equations with Atangana-Baleanu derivatives to a set of algebraic equations. When compared to previous methods, the numerical results validate the effectiveness of the suggested method as a robust mathematical tool, outperforming existing techniques in handling variable-order fractal-fractional varying-delay differential equations with an Atangana-Baleanu derivative.
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