A conformable calculus of radial basis functions and its applications

In this paper we introduced the conformable derivatives and integrals of radial basis functions (RBF) to solve conformable fractional differential equations via RBF collocation method. For that, firstly, we found the conformable derivatives and integrals of power, Gaussian and multiquadric basis functions utilizing the rule of conformable fractional calculus. Then by using these derivatives and integrals we provide a numerical scheme to solve conformable fractional differential equations. Finally we presents some numerical results to confirmed our method

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An efficient approach based on radial basis functions for solving stochastic fractional differential equations

Mathematical Sciences ◽

10.1007/s40096-017-0211-7 ◽

2017 ◽

Vol 11 (2) ◽

pp. 113-118 ◽

Cited By ~ 9

Author(s):

N. Ahmadi ◽

A. R. Vahidi ◽

T. Allahviranloo

Keyword(s):

Differential Equations ◽

Radial Basis Functions ◽

Fractional Differential Equations ◽

Basis Functions ◽

Efficient Approach ◽

Radial Basis ◽

Fractional Differential ◽

Stochastic Fractional Differential Equations

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Error estimate in fractional differential equations using multiquadratic radial basis functions

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2012.12.011 ◽

2013 ◽

Vol 245 ◽

pp. 133-147 ◽

Cited By ~ 14

Author(s):

B. Fakhr Kazemi ◽

F. Ghoreishi

Keyword(s):

Differential Equations ◽

Error Estimate ◽

Radial Basis Functions ◽

Fractional Differential Equations ◽

Basis Functions ◽

Radial Basis ◽

Fractional Differential

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On the numerical solution of fractional stochastic integro-differential equations via meshless discrete collocation method based on radial basis functions

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2018.05.006 ◽

2019 ◽

Vol 100 ◽

pp. 246-255 ◽

Cited By ~ 19

Author(s):

Farshid Mirzaee ◽

Nasrin Samadyar

Keyword(s):

Differential Equations ◽

Numerical Solution ◽

Collocation Method ◽

Radial Basis Functions ◽

Basis Functions ◽

Radial Basis

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Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations

Journal of Applied Mathematics ◽

10.1155/2012/542401 ◽

2012 ◽

Vol 2012 ◽

pp. 1-19 ◽

Cited By ~ 30

Author(s):

M. H. Heydari ◽

M. R. Hooshmandasl ◽

F. M. Maalek Ghaini ◽

F. Mohammadi

Keyword(s):

Differential Equations ◽

Collocation Method ◽

Fractional Differential Equations ◽

Initial Conditions ◽

General Procedure ◽

Wavelet Expansion ◽

Operational Matrices ◽

Chebyshev Wavelets ◽

Block Pulse Functions ◽

Fractional Differential

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by a change of variables, the multiorder fractional differential equations (MOFDEs) with nonhomogeneous initial conditions are transformed to the MOFDEs with homogeneous initial conditions to obtain suitable numerical solution of these problems. Numerical examples are provided to demonstrate the applicability and simplicity of the numerical scheme based on the Legendre and Chebyshev wavelets.

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Solving partial differential equations by meshless methods using radial basis functions

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.07.057 ◽

2007 ◽

Vol 185 (1) ◽

pp. 614-627 ◽

Cited By ~ 15

Author(s):

Yunxin Zhang

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Radial Basis Functions ◽

Meshless Methods ◽

Basis Functions ◽

Partial Differential ◽

Radial Basis

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An improved radial basis functions method for the high-order Volterra–Fredholm integro-differential equations

Mathematical Sciences ◽

10.1007/s40096-021-00432-2 ◽

2021 ◽

Author(s):

Farnaz Farshadmoghadam ◽

Haman Deilami Azodi ◽

Mohammad Reza Yaghouti

Keyword(s):

Differential Equations ◽

Radial Basis Functions ◽

High Order ◽

Basis Functions ◽

Radial Basis

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A meshless discrete collocation method for the numerical solution of singular-logarithmic boundary integral equations utilizing radial basis functions

Applied Mathematics and Computation ◽

10.1016/j.amc.2017.07.073 ◽

2017 ◽

Vol 315 ◽

pp. 424-444 ◽

Cited By ~ 5

Author(s):

Pouria Assari ◽

Mehdi Dehghan

Keyword(s):

Numerical Solution ◽

Integral Equations ◽

Collocation Method ◽

Radial Basis Functions ◽

Boundary Integral Equations ◽

Boundary Integral ◽

Basis Functions ◽

Radial Basis

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A numerical scheme for problems in fractional calculus

ITM Web of Conferences ◽

10.1051/itmconf/20182002001 ◽

2018 ◽

Vol 20 ◽

pp. 02001

Author(s):

M. Razzaghi

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Fractional Differential Equations ◽

Numerical Scheme ◽

Boundary Value ◽

Bernoulli Polynomials ◽

Algebraic Equations ◽

Hybrid Functions ◽

Block Pulse Functions ◽

Fractional Differential

In this paper, a new numerical method for solving the fractional differential equations with boundary value problems is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is given. This operator is then utilized to reduce the solution of the boundary value problems for fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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