THE CONSTRUCTION OF OPERATIONAL MATRIX OF FRACTIONAL DERIVATIVES USING B-SPLINE FUNCTIONS

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A review of operational matrices and spectral techniques for fractional calculus (2015, methodology): “Method of [78] 5 2.”
Numerical solution for a class of fractional convection–diffusion equations using the flatlet oblique multiwavelets (2014, methodology): “By considering Equation (17) we can write (Darani et al., 2010; Lakestani et al., 2006; Lakestani and Saray, 2010; Lakestani et al., 2011, 2012) f0ðxÞ ’ f T D ~ ðxÞ: ð21Þ So, by using the OMD, we can obtain the coefficients of expansion f0(x) from the coefficients of expansion f(x).”
A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials (2016, background): “Also the interested reader can see Dehghan et al. (2010), Eslahchi et al. (2014), Lakestani et al. (2012) and Saadatmandi and Dehghan (2010) for some research works on the numerical solution of fractional differential equations and applications.”
The Müntz-Legendre Tau method for fractional differential equations (2016, methodology): “In particular, we consider Pseudospectral method[14], Predictor-Corrector method[9], Spectral Tau method based on the classical orthogonal polynomials[11], Linear B-Spline method[25] and Legendre-collocation method[20].”
Optimal control problems with Atangana‐Baleanu fractional derivative (2020, background): “(43) By substituting Equations (35), (36), (40), and (41) into Equation (32), we get”