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.

Here, we synthesized three new blended ligand complexes of chromium (III), iron (III), and lanthanum (III) ions with a Schiff base made from the condensation of [o-aminophenol and 2-hydroxyacetophenone in the presence of concentrated sulphoric acid (HL1)] as a primary ligand and o-nitroaniline (L2) as a secondary. The Schiff base and its dual ligand chelate were characterized using several spectroscopic studies, IR, 1HNMR, electronic and mass spectra, in addition to elemental analyses, molar conductivity measurements, and magnetic moments. The spectroscopic and analytical outcomes confirmed the formation of the chelates in a 1:1:1(L1: M: L2) ratio. Similarly, an octahedral structure became counseled for all chelates.

This study was performd on 50 urine specimens of patients with type 2 diabetes, in addition, 50 normal specimens were investigated as control group. The activity rate of maltase in patients (6.40±2.17) I.U/ml and activity rate of maltase in normal (0.44±0.20)I.U/ml. The results of the study reveal that maltase activity of type 2 diabetes patient's urine shows significant increase (P<0.01) compare to normal.

I attended some amides non grassy substitutes such as acrylic compounds Amaid Electron Amaid and Alsinamamaid interaction unsaturated acids such as acrylic acid or Ketronk ????????? with primary amines Malkhtlfah of acrylic monomers Alamayd

New Schiff base ligand (E)-6-(2-(4-(dimethylamino)benzylideneamino)-2-(4-hydroxyphenyl)acetamido)-3,3- dimethyl-7-oxo-4-thia-1- azabicyclo[3.2.0]heptane-2-carboxylic acid = (HL) was synthesized via condensation of Amoxicillin and 4(dimethylamino)benzaldehyde in methanol. Figure -1 Polydentate mixed ligand complexes were obtained from 1:1:2 molar ratio reactions with metal ions and HL, 2NA on reaction with MCl2 .nH2O salt yields complexes corresponding to the formulas [M(L)(NA)2Cl],where M=Fe(II),Co(II),Ni(II),Cu(II),and Zn(II), A=nicotinamide .

This book includes four main chapters: 1. Indefinite Integral. 2. Methods of Integration. 3. Definite Integral. 4. Multiple Integral. In addition to many examples and exercises for the purpose of acquiring the student's ability to think correctly in solving mathematical questions.