Chain rules and inequalities for the BHT fractional calculus on arbitrary timescales

We develop the Benkhettou–Hassani–Torres fractional (noninteger order) calculus on timescales by proving two chain rules for the α-fractional derivative and five inequalities for the α-fractional integral. The results coincide with well-known classical results when the operators are of (integer) order α = 1 and the timescale coincides with the set of real numbers

Complex-valued fractional derivatives on time scales

We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.Comment: This is a preprint of a paper whose final and definite form will appear in Springer Proceedings in Mathematics & Statistics, ISSN: 2194-1009. Accepted for publication 06/Nov/201

DIVERSITÉ FLORISTIQUE DU MASSIF DU NADOR EN ZONE STEPPIQUE (TIARET, ALGÉRIE)

This study is devoted to Nador massif located in the steppe environment of Tiaret region in the west of Algeria. This massif is characterized by a diversity of flora composed of 121 taxa belonging to 38 families and 98 genera. Biological spectrum indicates a predominance of therophytes (38%) and chamaephytes (19%), geophytes (14%). The most important families are Poaceae and Asteraceae. Mediterranean element is relatively dominant (55%) according to chorologic plane. Shannon-Weaver e diversity index is relatively high (4.55) indicating a richly diverse site. Disturbance index (63.6%) reflects highly significant degree of massif vegetation disturbance, which also reflects a more open environment. To better understand the structure of vegetation using the classification is imperativ

Effect of multi-layer prosthetic foam liner on the stresses at the stump–prosthetic interface

The prosthetic liner plays a significant role in the redistribution of the pressure between the stump and the socket, as it adding a cushioning layer between the stump and the socket which relieves pain and makes the prosthesis more comfortable. This study employed nonlinear finite element analyses to investigate the peak pressure and shear stress at stump–prosthetic interface in the case of multi-layer prosthetic foam liner, this liner having an inner polymeric foam layer Surrounded by another type of polymeric foam layer, we used three different types of foams in different order to define this liner (flexible polyurethane foam, polyurethane-shape memory polymer foam, and natural rubber latex foam). That’s allows comparing 6 deferent configuration of multi-layer prosthetic foam liner.     &nbsp

Multi-objective Optimization of Multi-cells Foam Mattress

Body pressure dispersion mattresses are useful tools for preventing pressure ulcers in patients with limited mobility who experience prolonged body weight-related compression loads at their body contact areas over time. The objective of this study is to propose and optimize a multicell finite element (FE) model of foam mattress to prevent patients from developing pressure ulcers (bed sores), by improving the contact pressure distribution on the upper mattress surface and immersion in the mattress. The NSGA-II multi-objective genetic algorithm was used to predict different configurations of cell materials to provide a more comfortable sleep. Our mattress model contains many cells (50 × 50 × 50), each of which can contain one of the nine different foam firmnesses. The NSGA-II algorithm attempts to combine the properties of soft and firm foams into a single mattress. however, the complexity and intersection of the fitness function objectives and the high number of possible chances forced the optimal solutions set to extend into the area under the result of foams that have a compressive strength between soft and firm. Based on the overall optimization results, the standard deviation ranged from 0.00325 to 0.00175 MPa and the maximum mattress immersion ranged from 50 mm to less than 20 mm. Mattresses with optimal configurations disperse body pressure smoothly to fit the patient's body shape

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

Preliminary results on the effects of orthopedic implant stiffness fixed to the cut end of the femur on the stress at the stump-prosthetic interface

A lot of trans-femoral amputation patients experience skin breakdown due to the pressures and shear stresses in the stump-prosthesis interface. In this study, a finite element model was employed to investigate the stresses at the stump interface in the case of an orthopedic implant fixed to the cut end of the femur. By changing the stiffness of this implant, we aim to see how the stiffness of this implant affects the stresses in the interface between the amputated limb and the prosthesis. To find out the effects of implant stiffness, five values for the elastic modulus, ranging from 0.1 to 0.5 Mpa, with an interval of 0.1 Mpa were employed in the implant structure of the FE model. Obtained results show that the implant played important role in reducing the stresses at the stump-prosthesis interface where the contact pressure did not exceed 53 Kpa and 17.3 Kpa for shear stress in the stiffer case of an implant, while the contact pressure in the case of femur without implant exceeded 79Kpa and 42 Kpa for shear stress. We also noted that the intensity of the contact pressure and the shear stress is proportional to the stiffness of the implant, as the greater the implant stiffness, the higher the peak of these stresses

DIVERSITÉ FLORISTIQUE DU MASSIF DU NADOR EN ZONE STEPPIQUE (TIARET, ALGÉRIE)

This study is devoted to Nador massif located in the steppe environment of Tiaret region in the west of Algeria. This massif is characterized by a diversity of flora composed of 121 taxa belonging to 38 families and 98 genera. Biological spectrum indicates a predominance of therophytes (38%) and chamaephytes (19%), geophytes (14%). The most important families are Poaceae and Asteraceae. Mediterranean element is relatively dominant (55%) according to chorologic plane. Shannon-Weaver e diversity index is relatively high (4.55) indicating a richly diverse site. Disturbance index (63.6%) reflects highly significant degree of massif vegetation disturbance, which also reflects a more open environment. To better understand the structure of vegetation using the classification is imperativ

Existence and uniqueness of solution for a fractional Riemann-Liouville initial value problem on time scales

We introduce the concept of fractional derivative of Riemann-Liouville on time scales. Fundamental properties of the new operator are proved, as well as an existence and uniqueness result for a fractional initial value problem on an arbitrary time scale. © 2015 The Authors