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In this paper we define the right fractional derivative and its corresponding right fractional integral with exponential kernel. We provide the integration by parts formula and we use the Q -operator to confirm our results. The related Euler—Lagrange equations are obtained and one example is reported. Moreover, we formulate and discuss the discrete counterparts of our results. [ABSTRACT FROM AUTHOR]

In this paper we discuss an application of fractional variational calculus to the Basset-type fractional equations. It is well known that the unsteady motion of a sphere immersed in a Stokes fluid is described by an integro-differential equation involving derivative of real order. Here we study the inverse problem, i.e. we consider the problem from a Lagrangian point of view in the framework of fractional variational calculus. In this way we find an application of fractional variational methods to a classical physical model, finding a Basset-type fractional equation starting from a Lagrangian depending on derivatives of fractional order. [ABSTRACT FROM AUTHOR]

In this paper the fractional variational principles of constrained systems involving Riesz derivatives are discussed and one example is analyzed in detail. The fractional Euler-Lagrange equations of two fractional Lagrangians which differ by a fractional Riesz derivative are investigated. [Copyright &y& Elsevier]

The discrete Hamiltonian formulation of Lagrangian linear in velocities is investigated andthe equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed within discrete Lagrangian and Hamiltonian formulations for some systems with constraints. Three illustrative examples are investigated in details. [Copyright &y& Elsevier]

In this paper, the Chebyshev polynomials expansion method is applied to find both an analytical solution of the fractional transport equation in the one-dimensional plane geometry and its numerical approximations. The idea of the method is in reducing of the fractional transport equation to a system of the linear fractional differential equations for the unknown coefficients of the Chebyshev polynomials expansion. The obtained system of equations is then solved by using the operational method for the Caputo fractional derivative. [ABSTRACT FROM AUTHOR]

In this paper we investigate the fractional variational principles within Caputo derivatives in the presence of delay derivatives. The corresponding Euler-Lagrange equations are obtained for the case of one dependent variable. A generalization to n dependent variables is obtained. Physical example is analyzed in detail. [Copyright &y& Elsevier]