A numerical technique for solving multi-dimensional fractional optimal control problems

Abstract

In this article, we use the operation matrix (OM) of Riemann-Liouville fractional integral of the shifted Gegenbauer polynomials with the Lagrange multiplier method to provide efficient numerical solutions to the multi-dimensional fractional optimal control problems. The proposed technique transforms the under consideration problems into sets of nonlinear equations which are easy to solve. Numerical tests including numerical comparisons with some existing methods are introduced to demonstrate the accuracy and efficiency of the suggested technique.

Multitime multiobjective variational problems via η-approximation method

“…In 1932, the Physicist Dirac first introduced the term multitme, later used in mathematics [32,37]. The multitime control theory is related to the partial derivatives of dynamical systems and their optimization over multitime, also known as the multidimensional control problems, which have wide applications theoretically as well as numerically [1]. Multitime is the extension of single-time dynamic programming that contains m-dimensional evolution and path independent curvillinear integral functional was explained by Udriste and Tevy [38].…”

Numerical study on factional differential-algebraic systems by means of Chebyshev Pseudo spectral method

“…Nowadays, the fractional differential equations (FDEs) have gained increased appearances in varied problems in various fields of physics, chemistry, biology, applied science and engineering, this is due to their accuracy in modelling these problems [1][2][3][4][5][6][7][8]. Consequently, the development of analytical and numerical algorithms for FDEs is an interested topic for many researches [9][10][11][12][13][14][15][16].…”

Constructions of the optical solitons and other solitons to the conformable fractional Zakharov–Kuznetsov equation with power law nonlinearity

“…Nonetheless, numerous applications have been executed in the economy, quantum field theory, optical fibres, plasma physics, fluid mechanics, mathematical physics, biology, geochemistry, to mention a few. Thus, various mathematical methods have been improved to answer them, such as Lie symmetry analysis [1], the auxiliary equation method [2], the FRDTM [3], the tanφ(ξ )/2)-expansion method [4], Tanh method [5], the Riccati-Bernoulli sub-ODE method [6], the exp−φ(ξ )-expansion method [7][8][9], extended trial equation method [10], Fractional Fan sub-equation method [11], new generalized (G /G)-expansion method [12][13][14][15], exponential rational function method [16], (G /G)-expansion method [17][18][19], modified extended tanh method [20], improved (G /G)expansion method [21], differential transform method [22], the Painleve analysis [23], fractional homotopy method [24], Truncation method [25], Semi-Inverse variational principle [26], the Feng's first integral method [27], the unified method [28], G G 2 -expansion method [29], singular manifold method [30], singular manifold method [31], homotopy perturbation transform method [32], Collocation method [33], separation of variables method [34], Lagrange multiplier method [35], fractional Adams-Bashforth-Moulton method [36], Chebyshev wavelet method [37], Jacobi elliptic function method …”