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1. Introduction Since the introduction of fractional calculus of variations by Riewe [1], fractional calculus has been a subject of interest not only among mathematicians, but also among fluid mechanics, electricity and finance specialists, chemical physicists, biomedical engineering specialists, and control theory specialists. Considerable progress has been made to determine necessary and sufficient conditions that any extremal for the variational functional with fractional calculus must satisfy in recent years. R. Almeida [2] provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Almeida established the fractional Euler-Lagrange equations for the fundamental problem and when in presence of an integral constraint and Almeida obtained a Legendre condition. In [3] Almeida studied certain problems of calculus of variations that are dependent upon a Lagrange function on a Caputo-type fractional derivative; sufficient and necessary conditions of the first- and second-order are presented. In [4] Zhang Jianke, Ma Xiaojue, and Li Lifeng studied the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrange function depending on a Caputo-Fabrizio fractional derivative. In [5] Almeida et al. obtained necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative and indefinite integral. There has been a significant development in ordinary and partial fractional differential equations in recent years [6–9]. D. Tavares et al. in [10] presented two fractional isoperimetric problems where the Lagrangian depends on a combined Caputo derivative of variable fractional order and presented a new variational problem subject to holonomic constraint. Noether’s symmetry, namely, the invariance of Hamilton action under the infinitesimal transformations, is put forward for the first time by Noether [11]. In [12] Frederico et al. obtained a generalization of the Noether theorem for Lagrangians depending on mixed classical and Caputo derivatives that can be used to obtain constants of motion for dissipative systems. In [13] the Noether theorem and its inverse theorem for the nonlinear dynamical systems with nonstandard Lagrangians are studied. In [14] a variational principle for Lagrangian densities containing derivatives of real order was formulated and the invariance of this principle is studied in two characteristic cases. In [15] Yan B. et al. studied Noether’s symmetries and conserved quantities of the Birkhoffian systems in terms of fractional derivatives of variable order. 
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