Results 31 to 40 of about 1,463 (256)
Relationship Between the Nonlinear Oscillator and the Motor Cortex
IEEE Access, 2019 The investigations show that the fractional calculus could be employed for complex biological systems and capture intrinsic phenomena. At the same time, the research results also show that the neural network has the characteristics of fractional calculus
Qiang Lu
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Weighted Generalized Fractional Integration by Parts and the Euler–Lagrange Equation
Axioms, 2022 Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control.
Houssine Zine +3 more
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Matrix-variate statistical distributions and fractional calculus [PDF]
Fractional Calculus and Applied Analysis, 2011 A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established.
Mathai, A., Haubold, H.
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Weighted hypergeometric functions and fractional derivative
Advances in Difference Equations, 2017 We introduce some weighted hypergeometric functions and the suitable generalization of the Caputo fractional derivation. For these hypergeometric functions, some linear and bilinear relations are obtained by means of the mentioned derivation operator ...
JE Restrepo +3 more
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Generalized Multiparameters Fractional Variational Calculus [PDF]
International Journal of Differential Equations, 2012 This paper builds upon our recent paper on generalized fractional variational calculus (FVC). Here, we briefly review some of the fractional derivatives (FDs) that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs) which depend on two functions, and show that many of the one ...
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An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order
The Scientific World Journal, 2013 We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given.
Ricardo Almeida, Delfim F. M. Torres
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Fractional Tempered Variational Calculus
Mathematical Methods in the Applied SciencesABSTRACT In this paper, we derive sufficient conditions ensuring the existence of a weak solution for a tempered fractional Euler‐Lagrange equations. Furthermore, we study a fractional tempered version of Noether theorem, and we provide a very explicit expression of a constant of motion in terms of symmetry group and Lagrangian for ...
César E. Torres Ledesma +3 more
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A survey on fractional variational calculus [PDF]
, 2019 Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods. In particular, we provide necessary optimality conditions of Euler-Lagrange type for the fundamental, higher-order, and isoperimetric problems, and ...
Almeida, Ricardo, Torres, Delfim F. M.
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Fractional calculus of variations of several independent variables [PDF]
The European Physical Journal Special Topics, 2013 We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians depending on generalized partial integrals and derivatives. A generalized fractional Noether's theorem, a formulation
Odzijewicz, Tatiana +2 more
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Machines, 2023 The induction motor (IM) drives are prone to various uncertainties, disturbances, and non-linear dynamics. A high-performance control system is essential in the outer loop to guarantee the accurate convergence of speed and torque to the required value ...
Irfan Sami +6 more
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