Piecewise fractional Legendre functions for nonlinear fractional optimal control problems with ABC fractional derivative and non‐smooth solutions
Copyright policy )Piecewise fractional Legendre functions for nonlinear fractional optimal control problems with ABC fractional derivative and non‐smooth solutions
AbstractIn this study, to solve fractional problems with non‐smooth solutions (which include some terms in the form of piecewise or fractional powers), a new category of basis functions called the orthonormal piecewise fractional Legendre functions is introduced. The upper bound of the error of the series expansion of these functions is obtained. Two explicit formulas for computing the Riemann–Liouville and Atangana–Baleanu fractional integrals of these functions are derived. A direct method based on these functions and their fractional integral is proposed to solve a family of optimal control problems involving the ABC fractional differentiation whose solutions are non‐smooth in the above expressed forms. By the proposed technique, solving the original fractional problem turns into solving an equivalent system of algebraic equations. The established method accuracy is studied by solving some examples.
- Mississippi Valley State University United States
- Shiraz University of Technology Iran (Islamic Republic of)
Decomposition methods, non-smooth solutions, Atangana-Baleanu fractional derivative, Fractional ordinary differential equations, Atangana-Baleanu fractional integral, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), orthonormal piecewise fractional Legendre functions, Fractional derivatives and integrals, Optimality conditions for problems involving relations other than differential equations, optimal control problems, Riemann-Liouville fractional integral
Decomposition methods, non-smooth solutions, Atangana-Baleanu fractional derivative, Fractional ordinary differential equations, Atangana-Baleanu fractional integral, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), orthonormal piecewise fractional Legendre functions, Fractional derivatives and integrals, Optimality conditions for problems involving relations other than differential equations, optimal control problems, Riemann-Liouville fractional integral
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