Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics by Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres

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Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $$\Lambda $$ Λ CDM model by Ludovic Ducobu, Nicoleta Voicu

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Statement of the problem of designing a liquid rocket engine dual bell nozzle of the maximum thrust using the direct method of the calculus of variations by Ivan Dubrovskyi, Valerii Bucharskyi

“…As an alternative to the method of characteristics, this paper proposes to use the direct method of calculus of variations [4] for profiling a dual bell nozzle. …”
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Optimal trajectories in $L^1$ and under $L^1$ penalizations by Dumas, Annette, Santambrogio, Filippo

Subjects: “…non-autonomous calculus of variations…”
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Local estimates for functionals rotationally invariant with respect to the gradient by Telma João Santos

Subjects: “…calculus of variations…”
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Cohomology of the variational complex in the class of exterior forms of finite jet order by Gennadi Sardanashvily

“…In particular, this provides a solution of the global inverse problem of the calculus of variations of finite order on fiber bundles.…”
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Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations by Guanfeng Li, Yong Wang, Gejun Bao

“…We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous 𝒜-harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.…”
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A Note on the Semi-Inverse Method and a Variational Principle for the Generalized KdV-mKdV Equation by Li Yao, Yun-Jie Yang, Xing-Wei Zhou

“…Ji-Huan He systematically studied the inverse problem of calculus of variations. This note reveals that the semi-inverse method also works for a generalized KdV-mKdV equation with nonlinear terms of any orders.…”
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Efficient Variational Approaches for Deformable Registration of Images by Mehmet Ali Akinlar, Muhammet Kurulay, Aydin Secer, Mustafa Bayram

“…Image registration, an ill-posed optimization problem, is solved using a gradient-descent-based method and some fundamental theorems in calculus of variations. Euler-Lagrange equations with homogeneous Neumann boundary conditions are obtained. …”
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A Systematic Review on the Advancement in the Study of Fuzzy Variational Problems by Mansi Verma, Chuei Yee Chen, Adem Kılıçman, Risman Mat Hasim

“…In this paper, we provide a systematic review to recap the history of variational principle in the calculus of variations and compare it with the existing techniques in the fuzzy setting. …”
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Optimal Control of Polymer Flooding Based on Maximum Principle by Yang Lei, Shurong Li, Xiaodong Zhang, Qiang Zhang, Lanlei Guo

“…To cope with the optimal control problem (OCP) of this DPS, the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin’s weak maximum principle. …”
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Optimal Insurance Indemnity for the Insured with Low Risk Tolerance by Jiesong Zhang, Cailing Li

“…To overcome this challenge, we apply the calculus of variations method employing a variable upper limit that is related to the maximal risk level. …”
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Results on Solution Set in Certain Interval-Valued Controlled Models by Savin Treanţă, Omar Mutab Alsalami

“…The methodology used in this paper is a combination of techniques from the Lagrange–Hamilton theory, calculus of variations, and control theory. This study could be immediately improved by including an analysis of this class of optimization problems by using curvilinear integrals instead of multiple integrals. …”
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Bezier Curves Method for Fourth-Order Integrodifferential Equations by F. Ghomanjani, A. V. Kamyad, A. Kılıçman

“…Also, the presented method is developed for solving BVPs which arise from the problems in calculus of variation. These BVPs result from the Euler-Lagrange equations which are the necessary conditions of the extremums of problems in calculus of variation. …”
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