Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives
This paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators. We focus on variational problems involving the composition of functionals, deriving the Euler–Lagrange equation...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/3/188 |
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| _version_ | 1850090783911182336 |
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| author | Ricardo Almeida |
| author_facet | Ricardo Almeida |
| author_sort | Ricardo Almeida |
| collection | DOAJ |
| description | This paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators. We focus on variational problems involving the composition of functionals, deriving the Euler–Lagrange equation for this generalized case and providing optimality conditions for extremal curves. We explore problems with integral and holonomic constraints and consider higher-order derivatives, where the fractional orders are free. |
| format | Article |
| id | doaj-art-ddb8a056f34d4f869be7b0b342781942 |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-ddb8a056f34d4f869be7b0b3427819422025-08-20T02:42:30ZengMDPI AGFractal and Fractional2504-31102025-03-019318810.3390/fractalfract9030188Fractional Calculus of Variations for Composed Functionals with Generalized DerivativesRicardo Almeida0Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalThis paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators. We focus on variational problems involving the composition of functionals, deriving the Euler–Lagrange equation for this generalized case and providing optimality conditions for extremal curves. We explore problems with integral and holonomic constraints and consider higher-order derivatives, where the fractional orders are free.https://www.mdpi.com/2504-3110/9/3/188fractional calculuscalculus of variationsEuler–Lagrange equationisoperimetric problemholonomic problemtime delay |
| spellingShingle | Ricardo Almeida Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives Fractal and Fractional fractional calculus calculus of variations Euler–Lagrange equation isoperimetric problem holonomic problem time delay |
| title | Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives |
| title_full | Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives |
| title_fullStr | Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives |
| title_full_unstemmed | Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives |
| title_short | Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives |
| title_sort | fractional calculus of variations for composed functionals with generalized derivatives |
| topic | fractional calculus calculus of variations Euler–Lagrange equation isoperimetric problem holonomic problem time delay |
| url | https://www.mdpi.com/2504-3110/9/3/188 |
| work_keys_str_mv | AT ricardoalmeida fractionalcalculusofvariationsforcomposedfunctionalswithgeneralizedderivatives |