The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

Renal transplantation is a principal treatment option for end-stage kidney failure. Bone loss and fracture are serious complication of kidney transplantation, associated with morbidity and mortality. The pathogenesis of post transplantation bone loss is multifactorial and complex

Engineering equipment is essential part in the construction project and usually manufactured with long lead times, large costs and special engineering requirements. Construction manager targets that equipment to be delivered in the site need date with the right quantity, appropriate cost and required quality, and this entails an efficient supplier can satisfy these targets. Selection of engineering equipment supplier is a crucial managerial process .it requires evaluation of multiple suppliers according to multiple criteria. This process is usually performed manually and based on just limited evaluation criteria, so better alternatives may be neglected. Three stages of survey comprised number of public a

In recent years, polymeric nanomaterials have attracted much attention to the fields of optoelectronics and energy storage due to their unique properties. In this study, to improve limitations, such as moderate conductivity and limited stability of polyaniline (PANi), PANi /WO3 nanocomposites with different amounts of tungsten trioxide nanoparticles (2,5, 5 and 10 wt%) were synthesized and investigated. The samples were prepared using the rotation coating method and evaluated in structural tests (XRD, FTIR, FESEM), optical (UV-Visible, PL) and photosensitivity. The results showed that the presence of WO3 caused a gradual decrease in the energy band gap from 3.04 eV in pure PANi to 2.37 eV in the 10 wt% sample, which led to facilitating elec

This paper deals with the Magnetohydrodynyamic (Mill)) flow for a viscoclastic fluid of the generalized Oldroyd-B model. The fractional calculus approach is used to establish the constitutive relationship of the non-Newtonian fluid model. Exact analytic solutions for the velocity and shear stress fields in terms of the Fox H-function are obtained by using discrete Laplace transform. The effect of different parameter that controlled the motion and shear stress equations are studied through plotting using the MATHEMATICA-8 software.

New Fe(II),Co(II),Ni(II),Cu(II) and Zn(II) Schiff base complexes which have the molar ratio 2:1 metal to ligand of the general formula [M2( L) X4] (where L=bis(2-methyl furfuraldene)-4-4`-methylene bis(cyclo-hexylamine) ) were prepared by the reaction of the metal salts with the ligand of Schiff base derived from the condensation of 2:1 molar ratio of 2-acetyl furan and 4-4`-methylene bis (cyclohexylamine). The complexes were characterized by elemental analysis using atomic absorption spectrophotometer ,molar conductance measurements, infrared, electronic spectra,and magnetic susceptibility measurement. These studies revealed binuclear omplexes. The metal(II) ion in these complexes have four coordination sites giving the most ex