scholarly journals Higher-Order Geodesic Equations from Non-Local Lagrangians and Complex Backward-Forward Derivative Operators

2016 ◽  
Vol 54 (1) ◽  
pp. 139-157
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
Differential Geometry ◽  
Higher Order ◽  
Order Derivative ◽  
Lagrangian Dynamics ◽  
Derivative Operator ◽  
Geodesic Equations ◽  
Non Local ◽  
Extended Complex

Abstract Starting with an extended complex backwardforward derivative operator in differential geometry which is motivated from non-local-in-time Lagrangian dynamics, higher-order geodesic equations are obtained within classical differential geometrical settings. We limit our analysis up to the 2nd-order derivative where some applications are discussed and a number of features are revealed accordingly.

scholarly journals PID Control With Higher Order Derivative Degrees for IPDT Plant Models

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 2478-2495
Author(s):  
Mikulas Huba ◽  
Damir Vrancic ◽  
Pavol Bistak
Keyword(s):  
Pid Control ◽  
Higher Order ◽  
Order Derivative ◽  
Higher Order Derivative

scholarly journals Generalizations and applications of Young’s integral inequality by higher order derivatives

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jun-Qing Wang ◽  
Bai-Ni Guo ◽  
Feng Qi
Keyword(s):  
Differential Geometry ◽  
Integral Inequality ◽  
Higher Order ◽  
Integral Inequalities ◽  
List Type ◽  
Definite Integral ◽  
Exponential Integral ◽  
Definite Integrals ◽  
Logarithmic Integral

Abstract In the paper, the authors generalize Young’s integral inequality via Taylor’s theorems in terms of higher order derivatives and their norms, and apply newly-established integral inequalities to estimate several concrete definite integrals, including a definite integral of a function which plays an indispensable role in differential geometry and has a connection with the Lah numbers in combinatorics, the exponential integral, and the logarithmic integral.

scholarly journals Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Mostafa Tahiri ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Optimality Conditions ◽  
Fractional Derivatives ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Derivative Operator ◽  
Sir Epidemic ◽  
Non Local

<p style='text-indent:20px;'>The main aim of the present work is to study and analyze a reaction-diffusion fractional version of the SIR epidemic mathematical model by means of the non-local and non-singular ABC fractional derivative operator with complete memory effects. Existence and uniqueness of solution for the proposed fractional model is proved. Existence of an optimal control is also established. Then, necessary optimality conditions are derived. As a consequence, a characterization of the optimal control is given. Lastly, numerical results are given with the aim to show the effectiveness of the proposed control strategy, which provides significant results using the AB fractional derivative operator in the Caputo sense, comparing it with the classical integer one. The results show the importance of choosing very well the fractional characterization of the order of the operators.</p>

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