Calculus of variations with higher order Caputo fractional derivatives. (English) Zbl 1542.49024
Reviewer: Roberto Garra (Roma)
Found 100 Documents (Results 1–100)
General fractional classical mechanics: action principle, Euler-Lagrange equations and Noether theorem. (English) Zbl 07808029
Conservation laws for systems of non-standard Birkhoffians with fractional derivatives. (English) Zbl 07793540
Transmutation operators intertwining first-order and distributed-order derivatives. (English) Zbl 1530.35353
Properties of fractional calculus with respect to a function and Bernstein type polynomials. (English) Zbl 1541.26031
Novel and accurate Gegenbauer spectral tau algorithms for distributed order nonlinear time-fractional telegraph models in multi-dimensions. (English) Zbl 1508.65138
Reviewer: Marius Ghergu (Dublin)
Time fractional super KdV equation: Lie point symmetries, conservation laws, explicit solutions with convergence analysis. (English) Zbl 1541.35538
On solvability for a class of nonlinear systems of differential equations with the Caputo fractional derivative. (English) Zbl 1503.34022
A one-phase space-fractional Stefan problem with no liquid initial domain. (English) Zbl 1501.35446
Reviewer: Mohammed El Aïdi (Bogotá)
Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. (English) Zbl 1487.49027
Optimality conditions involving the Mittag-Leffler tempered fractional derivative. (English) Zbl 1497.49009
Reviewer: Alain Brillard (Riedisheim)
Noether’s theorem for Herglotz type variational problems utilizing complex fractional derivatives. (English) Zbl 07804661
Optimality conditions for variational problems involving distributed-order fractional derivatives with arbitrary kernels. (English) Zbl 1484.49039
Noether symmetry method for Hamiltonian mechanics involving generalized operators. (English) Zbl 1501.26007
Reviewer: Giovanni Rastelli (Vercelli)
Noether’s theorem for variational problems of Herglotz type with real and complex order fractional derivatives. (English) Zbl 1492.49022
Legendre’s necessary condition for fractional Bolza functionals with mixed initial/final constraints. (English) Zbl 1471.49017
Two unconditionally stable difference schemes for time distributed-order differential equation based on Caputo-Fabrizio fractional derivative. (English) Zbl 1487.65119
On the thermodynamical restrictions in isothermal deformations of fractional Burgers model. (English) Zbl 1462.74029
Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 378, No. 2172, Article ID 20190278, 13 p. (2020).
Adiabatic invariants for disturbed fractional Hamiltonian system in terms of Herglotz differential variational principle. (English) Zbl 1457.70025
Wave propagation dynamics in a fractional Zener model with stochastic excitation. (English) Zbl 1488.35324
On the transient response of plates on fractionally damped viscoelastic foundation. (English) Zbl 1474.74108
Noether symmetries for fractional generalized Birkhoffian systems in terms of classical and combined Caputo derivatives. (English) Zbl 1440.70011
Fractional calculus of variations: a novel way to look at it. (English) Zbl 1439.49045
Reviewer: Suvra Kanti Chakraborty (Kolkata)
About the Noether’s theorem for fractional Lagrangian systems and a generalization of the classical Jost method of proof. (English) Zbl 1473.70038
Variational problems of Herglotz type with complex order fractional derivatives and less regular Lagrangian. (English) Zbl 1431.26006
Discussing the extension and applications of a variational approach with deformed derivatives. (English) Zbl 1434.49016
Analysis and numerical approximation of tempered fractional calculus of variations problems. (English) Zbl 1425.49015
Fractional telegrapher’s equation as a consequence of Cattaneo’s heat conduction law generalization. (English) Zbl 1474.35601
Geometry of curves with fractional-order tangent vector and Frenet-Serret formulas. (English) Zbl 1428.53011
Stability analysis of Beck’s column over a fractional-order hereditary foundation. (English) Zbl 1407.74051
Invariance properties, conservation laws, and soliton solutions of the time-fractional \((2+1)\)-dimensional new coupled ZK system in magnetized dusty plasmas. (English) Zbl 1424.35347
Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws. (English) Zbl 1445.35298
Noether symmetry and conserved quantity for fractional Birkhoffian mechanics and its applications. (English) Zbl 1437.70026
Properties of the Caputo-Fabrizio fractional derivative and its distributional settings. (English) Zbl 1392.26010
Fractional bosonic strings. (English) Zbl 1384.81085
On a constitutive equation of heat conduction with fractional derivatives of complex order. (English) Zbl 1384.74004
Optimality conditions for fractional variational problems with free terminal time. (English) Zbl 1379.49014
Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives. (English) Zbl 1538.34087
Space-time fractional nonlinear partial differential equations: symmetry analysis and conservation laws. (English) Zbl 1374.35429
Variational problems involving a Caputo-type fractional derivative. (English) Zbl 1379.26009
Reviewer: Vyacheslav I. Maksimov (Ekaterinburg)
A simple accurate method for solving fractional variational and optimal control problems. (English) Zbl 1377.49016
Variational problem of Herglotz type for Birkhoffian system and its Noether’s theorems. (English) Zbl 1401.70028
Anomalous convection diffusion and wave coupling transport of cells on comb frame with fractional Cattaneo-Christov flux. (English) Zbl 1458.76095
Fractional calculus of variations with a generalized fractional derivative. (English) Zbl 1438.49035
Lie symmetries and their inverse problems of nonholonomic Hamilton systems with fractional derivatives. (English) Zbl 1377.70032
A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials. (English) Zbl 1365.26005
Noether symmetries and conserved quantities for fractional forced Birkhoffian systems. (English) Zbl 1359.37130
Numerical solution for fractional variational problems using the Jacobi polynomials. (English) Zbl 1443.49039
Existence results for fractional-order differential equations with nonlocal multi-point-strip conditions involving Caputo derivative. (English) Zbl 1422.34014
Perturbation to Noether symmetries and adiabatic invariants for Birkhoffian systems. (English) Zbl 1394.70050
A new approach on fractional variational problems and Euler-Lagrange equations. (English) Zbl 1351.49020
Fractional variational symmetries of Lagrangians, the fractional Galilean transformation and the modified Schrödinger equation. (English) Zbl 1347.26020
Noether symmetries and conserved quantities for fractional Birkhoffian systems. (English) Zbl 1347.26027
Dynamics of a fractional derivative type of a viscoelastic rod with random excitation. (English) Zbl 1428.74100
Conservation laws for time-fractional subdiffusion and diffusion-wave equations. (English) Zbl 1345.35131
Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order. (English) Zbl 1317.49022
Fractional Noether theorem based on extended exponentially fractional integral. (English) Zbl 1302.70055
Noether’s theorem for fractional variational problem from El-Nabulsi extended exponentially fractional integral in phase space. (English) Zbl 1356.70023
Forced oscillations of a body attached to a viscoelastic rod of fractional derivative type. (English) Zbl 1423.74173
A generalized fractional variational problem depending on indefinite integrals: Euler-Lagrange equation and numerical solution. (English) Zbl 1358.93098
On reflection symmetry and its application to the Euler-Lagrange equations in fractional mechanics. (English) Zbl 1342.26023
Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 371, No. 1990, Article ID 20120145, 15 p. (2013).
Reflection symmetric formulation of generalized fractional variational calculus. (English) Zbl 1312.26015
Symmetries and conserved quantities for fractional action-like Pfaffian variational problems. (English) Zbl 1281.58002
Reflection symmetry in fractional calculus – properties and applications. (English) Zbl 1276.26015
Mitkowski, Wojciech (ed.) et al., Advances in the theory and applications of non-integer order systems. 5th conference on non-integer order calculus and its applications, Cracow, Poland, July 4–5, 2013. Cham: Springer (ISBN 978-3-319-00932-2/hbk; 978-3-319-00933-9/ebook). Lecture Notes in Electrical Engineering 257, 201-211 (2013).
MSC:
26A33
The Cattaneo type space-time fractional heat conduction equation. (English) Zbl 1267.80006
Reviewer: Mersaid Aripov (Tashkent)
A formulation of the fractional Noether-type theorem for multidimensional Lagrangians. (English) Zbl 1259.49005
Multiobjective fractional variational calculus in terms of a combined Caputo derivative. (English) Zbl 1238.49029
Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives. (English) Zbl 1221.49038
Thermodynamical restrictions and wave propagation for a class of fractional order viscoelastic rods. (English) Zbl 1217.74064
A fractional calculus of variations for multiple integrals with application to vibrating string. (English) Zbl 1309.49003
Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative. (English) Zbl 1193.49023
On the global existence of solutions to a class of fractional differential equations. (English) Zbl 1189.34006
Calculus of variations with fractional derivatives and fractional integrals. (English) Zbl 1183.26005
MSC:
26A33
Complexified fractional heat kernel and physics beyond the spectral triplet action in noncommutative geometry. (English) Zbl 1179.58002
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