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Fractional calculus of variations with a generalized fractional derivative [PDF]
Fractional Differential Calculus, 2016 Summary: In this paper, we introduce a generalization of the Hilfer-Prabhakar derivative and obtain the Euler-Lagrange equations and Hamiltonian formulation with respect to this fractional derivative in the theory of fractional calculus of variations. Also, we get a sufficient condition for optimality.
Askari, Hassan, Ansari, Alireza
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Construction and Evaluation of a Control Mechanism for Fuzzy Fractional-Order PID
Applied Sciences, 2022 In this research, a control mechanism for fuzzy fractional-order proportional integral derivatives was suggested (FFOPID). The fractional calculus application has been used in different fields of engineering and science and showed to be improved in the ...
Mujahed Al-Dhaifallah
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Axioms, 2023 In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor.
Jindong Liu +4 more
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Advances in Difference Equations, 2017 In this paper, we study the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrange function depending on a Caputo-Fabrizio fractional derivative.
Jianke Zhang, Xiaojue Ma, Lifeng Li
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Heliyon, 2021 Wind energy is considered as one of the rapidest rising renewable energy systems. Thus, in this paper the wind energy performance is enhanced through using a new adaptive fractional order PI (AFOPI) blade angle controller.
Ahmed M. Shawqran +4 more
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Journal of Function Spaces, 2018 We study in this paper the Atangana-Baleanu fractional derivative of fuzzy functions based on the generalized Hukuhara difference. Under the condition of gH-Atangana-Baleanu fractional differentiability, we prove the generalized necessary and sufficient ...
Jianke Zhang +3 more
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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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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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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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