Results 241 to 247 of about 383,064 (247)

Approximations of fractional integrals and Caputo fractional derivatives

Applied Mathematics and Computation, 2006
Abstract In this paper we propose two algorithms for numerical fractional integration and Caputo fractional differentiation. We present a modification of trapezoidal rule that is used to approximate finite integrals, the new modification extends the application of the rule to approximate integrals of arbitrary order α > 0.
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On a New Extension of Caputo Fractional Derivative Operator

2017
In this paper, by using a generalization of beta function we introduced a new extension of Caputo fractional derivative operator and obtained some of its properties. With the help of this extended fractional derivative operator, we also defined new extensions of some hypergeometric functions and determined their integral representations, linear and ...
Kıymaz İ.O., Agarwal P., Jain S., Çetinkaya A.   +3 more
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Fractional Constrained Systems and Caputo Derivatives

Journal of Computational and Nonlinear Dynamics, 2008
During the last few years, remarkable developments have been made in the theory of the fractional variational principles and their applications to control problems and fractional quantization issue. The variational principles have been used in physics to construct the phase space of a fractional dynamical system.
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Fractional Optimal Control Within Caputo’s Derivative

Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B, 2011
A general formulation and solution of fractional optimal control problems (FOCPs) in terms of Caputo fractional derivatives (CFDs) of arbitrary order have been considered in this paper. The performance index (PI) of a FOCP is considered as a function of both the state and control.
Siddhartha Sen, Raj Kumar Biswas
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On Fractional Hamilton Formulation Within Caputo Derivatives

Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 2007
The fractional Lagrangian and Hamiltonian dynamics is an important issue in fractional calculus area. The classical dynamics can be reformulated in terms of fractional derivatives. The fractional variational principles produce fractional Euler-Lagrange equations and fractional Hamiltonian equations.
Sami I. Muslih, Eqab M. Rabei, Dumitru Baleanu   +2 more
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The Caputo Fractional Δ-Derivative on Time Scales

2018
In this chapter we suppose that \(\mathbb {T}\) is a time scale with forward jump operator and delta differentiation operator σ and Δ, respectively.
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A Fast Algorithm for the Caputo Fractional Derivative

East Asian Journal on Applied Mathematics, 2018
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