Nonlinear Numerical Analysis in Reproducing Kernel Space

By M. Cui, Yingzhen Lin. 2009

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Adaptation of kernel functions‐based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations (2021, unknown): “It is to be noted here, in the phase of Equation (22), we have z1η,z2η ∈ DR  ð Þ together with D(1)t z t ð Þ η = z1η t ð Þ,z2η t ð Þ h i , while in the phase of Equation (23), we have z1η,z2η ∈ DR  ð Þ together with D(2)t z t ð Þ η = z2η t ð Þ,z1η t ð Þ h i :”
Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis (2019, methodology): “k1⁄41 μ lk Fk tl; w ! tl ð Þ ; : 8><>>: (22)”
Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method (2015, methodology): “Reproducing kernel theory has important application in numerical analysis, computational mathematics, image processing, machine learning, ﬁnance, and probability and statistics (Berlinet and Agnan 2004; Cui and Lin 2009; Daniel 2003; Weinert 1982).”