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Conformable Fractional Gradient Based Dynamic System for Constrained Optimization Problem

100%

Evirgen F.

Acta Physica Polonica A

2017

vol. 132

issue 3

1066-1069

A conformable fractional gradient based dynamic system with a steepest descent direction is proposed in this paper for a class of nonlinear programming problems. The solutions of the dynamic system, modelled with the conformable fractional derivative are investigated to obtain the minimizing point of the optimization problem. For this purpose, we use a step variational iteration method, adapted to use a conformable integral definition. Numerical simulations and comparisons show that the conformable fractional gradient based dynamic system is both feasible and efficient for a certain class of equality constrained optimization problems. Furthermore, the step variational iteration method, combined with the conformable integral definition, is a reliable tool for solving a system of fractional differential equations.

Fractional Newtonian mechanics

64%

Baleanu D., Golmankhaneh A., Nigmatullin R., Golmankhaneh A.

Open Physics

2010

vol. 8

issue 1

120-125

In the present paper, we have introduced the generalized Newtonian law and fractional Langevin equation. We have derived potentials corresponding to different kinds of forces involving both the right and the left fractional derivatives. Illustrative examples have worked out to explain the formalism.

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1 Acta Physica Polonica A

1 Open Physics

1 2017

1 2010

1 Baleanu D.

1 Evirgen F.

1 Golmankhaneh A.

1 Nigmatullin R.

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Conformable Fractional Gradient Based Dynamic System for Constrained Optimization Problem

Fractional Newtonian mechanics