Variable order Mittag-Leffler fractional operators on isolated time scales and application to the calculus of variations

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main results give fractional integration by parts formulas and necessary optimality conditions of Euler-Lagrange type.Comment: This is a preprint of a paper whose final and definite form is with Springe

Kinematic analysis of the daily activity of drinking from a glass in a population with cervical spinal cord injury

Background Three-dimensional kinematic analysis equipment is a valuable instrument for studying the execution of movement during functional activities of the upper limbs. The aim of this study was to analyze the kinematic differences in the execution of a daily activity such as drinking from a glass between two groups of patients with tetraplegia and a control group. Methods A total of 24 people were separated into three groups for analysis: 8 subjects with metameric level C6 tetraplegia, 8 subjects with metameric level C7 tetraplegia and 8 control subjects (CG). A set of active markers that emit infrared light were positioned on the upper limb. Two scanning units were used to record the sessions. The activity of drinking from a glass was broken down into a series of clearly identifiable phases to facilitate analysis. Movement times, velocities, and the joint angles of the shoulder, elbow and wrist in the three spatial planes were the variables analyzed. Results The most relevant differences between the three groups were in the wrist. Wrist palmar flexion during the back transport phase was greater in the patients with C6 and C7 tetraplegia than in the CG, whereas the highest wrist dorsal flexion values were in forward transport in the subjects with C6 or C7 tetraplegia, who required complete activation of the tenodesis effect to complete grasping. Conclusions A detailed description was made of the three-dimensional kinematic analysis of the task of drinking from a glass in healthy subjects and in two groups of patients with tetraplegia. This was a useful application of kinematic analysis of upper limb movement in a clinical setting. Better knowledge of the execution of this movement in each of these groups allows therapeutic recommendations to be specifically adapted to the functional deficit present. This information can be useful in designing wearable robots to compensate the performance of AVD, such as drinking, in people with cervical SCI