The Duality Theory of Fractional Calculus and a New Fractional Calculus of Variations Involving Left Operators Only
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DOI: 10.1007/s00009-024-02652-x
Abstract: Through duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right… read more here.
Keywords: theory fractional; calculus variations; fractional calculus; calculus new ... See more keywords
A new functional for the Calculus of Variations, involving the variational mean curvature of sets in $$R^n$$Rn
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DOI: 10.1007/s00229-017-0985-9
Abstract: We study the pth power $$W_p(E)=\int _{{\mathbb R}^n}|H_E|^p\,dx$$Wp(E)=∫Rn|HE|pdx, where $$H_E$$HE is the variational mean curvature of E, as defined in Barozzi (Rend Mat Acc Linceis 9(5):149–159, 1994) (see also in Proc Am Math Soc 99:313–316,… read more here.
Keywords: variational mean; mean curvature; functional calculus; new functional ... See more keywords
On a degenerate problem in the calculus of variations
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DOI: 10.1090/tran/7570
Abstract: We establish the uniqueness of the solutions for a degenerate scalar problem in the multiple integrals calculus of variations. The proof requires as a preliminary step the study of the regularity properties of the solutions… read more here.
Keywords: calculus variations; problem; degenerate problem; problem calculus ... See more keywords
Bernstein polynomials method and it’s error analysis for solving nonlinear problems in the calculus of variations: Convergence analysis via residual function
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DOI: 10.2298/fil1804379b
Abstract: In this paper, Bernstein polynomials method (BPM) and their operational matrices are adopted to obtain approximate analytical solutions of variational problems. The operational matrix of differentiation is introduced and utilized to reduce the calculus of… read more here.
Keywords: analysis; bernstein polynomials; polynomials method; residual function ... See more keywords