Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space

A new numerical method for singularly perturbed turning point problems with two boundary layers based on reproducing kernel method

“…Recently, based on the reproducing kernel theory, a method called the reproducing kernel method for solving operator equations (RKM) was proposed by Geng and Cui [10], Cui and Geng [11] and Cui et al [12]. Recently, the method has been applied to many fields [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

The Reproducing Kernel Method for Some Variational Problems Depending on Indefinite Integrals

“…The theory of reproducing kernels [2] was used for the first time at the beginning of the 20th century by S. Zaremba in his work on boundary value problems for harmonic and biharmonic functions. This theory has been successfully applied to fractal interpolation [6], solving ordinary differential equations [3,4,8,14,15,18,19,20,22,30,31] and partial differential equations [7,24]. The books [5,9,11] provide an excellent overview of the existing reproducing kernel methods for solving various model problems such as integral and integrodifferential equations.…”

Solving nonlocal initial‐boundary value problems for parabolic and hyperbolic integro‐differential equations in reproducing kernel hilbert space

“…In [7] authors have proved the existence, uniqueness and continuous dependence on the data of solution for (15)- (17).…”

“…Geng and Cui [16] applied the reproducing kernel method to handle the nonlocal fractional boundary value problems. Recently, the Hilbert function space was applied for solving the nonlinear delay differential equations of fractional order [17]. Jiang and Cui [18] applied the reproducing kernel method to obtain the exact solution of the nonlinear Volterra-Fredholm integral equations using the reproducing kernel Hilbert space method.…”