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Article
Fractional calculus of variations of several independent variables
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 variationa...
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Chapter and Conference Paper
Fractional Variational Calculus of Variable Order
We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann–Liouville while derivatives are of Caputo type.
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Article
The Hahn Quantum Variational Calculus
We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Le...
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Article
Avoidance Control on Time Scales
We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent’s actions. Leitmann’s avoi...
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Article
Necessary and sufficient conditions for local Pareto optimality on time scales
We study a multiobjective variational problem on time scales. For this problem, necessary and sufficient conditions for weak local Pareto optimality are given. We also prove a necessary optimality condition fo...
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Article
On the two-dimensional rotational body of maximal Newtonian resistance
We investigate, by means of computer simulations, shapes of nonconvex bodies that maximize resistance to their motion through a rarefied medium, considering that the bodies are moving forward and at the same t...
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Article
Combined dynamic Grüss inequalities on time scales
We prove a more general version of the Grüss inequality by using the recent theory of combined dynamic derivatives on time scales and the more general notions of diamond-α derivative and integral. For the particu...
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Article
Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization
The question of obtaining well-defined criteria for multiple-criteria decision making problems is well known. One of the approaches dealing with this question is the concept of nonessential objective functions...
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Article
Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema
In this note, we contrast two transformation-based methods to deduce absolute extrema and the corresponding extremizers. Unlike variation-based methods, the transformation-based methods of Carlson and Leitman...
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Article
Necessary Optimality Conditions for a Dead Oil Isotherm Optimal Control Problem
We study a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of the mechanics of a continuous medium. Recent results on the pr...
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Article
Carathéodory Equivalence, Noether Theorems, and Tonelli Full-Regularity in the Calculus of Variations and Optimal Control
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Article
Lipschitzian Regularity of Minimizers for Optimal Control Problems with Control-Affine Dynamics
We study the Lagrange Problem of Optimal Control with a functional \(\int_{a}^{b}L\left(t,\,x\left(t\right),\,u\left(t\right)\right)\,dt\) and control-affine dynamics ...
