Approximate solutions of Atangana-Baleanu variable order fractional problems
Xiuying Li, Yang Gao, Boying Wu
Abstract
The main aim of this paper is to propose a new approach for Atangana-Baleanu variable order fractional problems. We introduce a new reproducing kernel function with polynomial form. The advantage is that its fractional derivatives can be calculated explicitly. Based on this kernel function, a new collocation technique is developed for variable order fractional problems in the Atangana-Baleanu fractional sense. To show the accuracy and effectiveness of our approach, we provide three numerical experiments.
Topics & Concepts
MathematicsVariable (mathematics)Kernel (algebra)Applied mathematicsOrder (exchange)Function (biology)Fractional calculusPolynomialCollocation (remote sensing)Mathematical optimizationMathematical analysisComputer sciencePure mathematicsBiologyFinanceMachine learningEconomicsEvolutionary biologyFractional Differential Equations SolutionsMathematical functions and polynomialsNonlinear Differential Equations Analysis