LEADER 05218nam 22008775 450 001 9910299767303321 005 20220406231405.0 010 $a3-319-14756-0 024 7 $a10.1007/978-3-319-14756-7 035 $a(CKB)3710000000355406 035 $a(EBL)1974103 035 $a(SSID)ssj0001452127 035 $a(PQKBManifestationID)11789710 035 $a(PQKBTitleCode)TC0001452127 035 $a(PQKBWorkID)11487834 035 $a(PQKB)10621694 035 $a(DE-He213)978-3-319-14756-7 035 $a(MiAaPQ)EBC1974103 035 $a(PPN)184495377 035 $a(EXLCZ)993710000000355406 100 $a20150205d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAdvanced methods in the fractional calculus of variations /$fby Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (142 p.) 225 1 $aSpringerBriefs in Applied Sciences and Technology,$x2191-530X 300 $aDescription based upon print version of record. 311 $a3-319-14755-2 320 $aIncludes bibliographical references and index. 327 $a1. Introduction -- 2. Fractional Calculus -- 3. Fractional Calculus of Variations -- 4. Standard Methods in Fractional Variational Calculus -- 5. Direct Methods in Fractional Calculus of Variations -- 6. Application to the Sturm-Liouville Problem -- 7. Conclusion -- Appendix - Two Convergence Lemmas -- Index. 330 $aThis brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler?Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler?Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm?Liouville problems. Advanced Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering. 410 0$aSpringerBriefs in Applied Sciences and Technology,$x2191-530X 606 $aCalculus of variations 606 $aAutomatic control 606 $aPhysics 606 $aEconomics 606 $aMathematical models 606 $aSystem theory 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aEconomic Theory/Quantitative Economics/Mathematical Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/W29000 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 615 0$aCalculus of variations. 615 0$aAutomatic control. 615 0$aPhysics. 615 0$aEconomics. 615 0$aMathematical models. 615 0$aSystem theory. 615 14$aCalculus of Variations and Optimal Control; Optimization. 615 24$aControl and Systems Theory. 615 24$aMathematical Methods in Physics. 615 24$aEconomic Theory/Quantitative Economics/Mathematical Methods. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aSystems Theory, Control. 676 $a003.3 676 $a330 676 $a330.0151 676 $a510 676 $a515.64 676 $a519 676 $a530.15 676 $a629.8 700 $aMalinowska$b Agnieszka B$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755557 702 $aOdzijewicz$b Tatiana$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTorres$b Delfim F.M$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910299767303321 996 $aAdvanced Methods in the Fractional Calculus of Variations$92546582 997 $aUNINA