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.

A new carbonyl complexes of triazole and oxadiazole were synthesized. These complexes were identified and their structural geometric were suggested by using FT-IR and UV-Vis spectra, conductivity measurements and other chemical and physical properties. The spectra data (FT-IR, UV, Vis.) with the substantial aid of group theoretical calculations gave so many evidences for the proposed geometries and the type of bonding of these compounds

Newly acid hydrazide was synthesized from ethyl 2-(2,3-dimethoxyphenoxy) acetate (2), which is cyclized to the corresponding  4-amino-1,2,4-triazole (3). Five newly azo derivatives (4a-e) were synthesized from this 1,2,4-triazole by converting the amine group to diazonium salt then reacted with various substituent phenol,as well three newly imine derivatives (5a-c) were synthesized from reacting the amine group of compound (3) with three aryl aldehyde. The thermal electro conductivity of these compounds was tested at 30, 50, 75 and 100 áµ’C. compound 4a showed interesting electro conductivity at 75áµ’C as well 5a at 75áµ’C while 5b showed significant conductivity at 100 áµ’C

A new series of 5-methoxy-2-mercapto benzimidazole derivatives were synthesized by the reaction of 5-methoxy- 2-mercaptobenzimidazole with chloroacetic acid and affords 2-((5-methoxy-1H-benzo[d]imidazol-2-yl)thio) acetic acid (1),which on cyclization with acetic anhydride and pyridine gives 7- methoxybenzo[4,5]imidazo[2,1-b]thiazol- 3(2H)-one(2), which on condensation with different aryl aldehydes in the presence of anhydrous sodium acetate in glacial acetic acid, furnishes a arylidene thiazolidinone. The purity of the synthesized compounds was confirmed by melting point and TLC.The structures were established by different spectral analysis such as FTIR,1HNMR, and CHN analysis. The newly synthesized compounds (3a-d) were in vivo evaluated f

Nonsteroidal anti-inflammatory drugs (NSAIDs) are drugs that help reduce inflammation, which often helps to relieve pain. In this research new ibuprofen oxothiazolidnone derivatives were synthesized from the reaction of Schiff base derivatives of Ibuprofen with mercapto acetic acid VI a-c, to improve the potency and to decrease the drug's potential side effects, a new series of 4-thiazolidinone derivatives of ibuprofen was synthesized VI a-c . The characterizations of the compounds were identified by using FTIR, 1HNMR technique and by measuring the physical properties.

Heterocyclic systems, which are essential in medicinal chemistry due to their promising cytotoxic activity, are one of the most important families of organic molecules found in nature or produced in the laboratory. As a result of coupling N-(4-nitrophenyl)-3-oxo-butanamide (3) using thiourea, indole-3-carboxaldehyde, or piperonal, the pyrimidine derivatives (5a and 5b) were produced. Furthermore, pyrimidine 9 was synthesized by reacting thiophene-2-carboxaldehyde with ethyl cyanoacetate and urea with potassium carbonate as a catalyst. The chalcones 11a and 11b were synthesized by reacting equal molar quantities of 1-naphthaldehy

Objective: Synthesis, Characterization of formazan derivatives and studies the antioxidant activity of prepared compounds and molecular docking. Methods: In this study, formazan compounds (III–XIV) were produced by combining Schiff base compounds (I), (II) with diazonium salts resulting from reactions of different aromatic amines with sodium nitrate in the presence of Con.HCl at 0–5°C. When isonicotinic acid hydrazide reacts with (N,N-dimethylbenzaldehyde, 4-hydroxy-3-methoxybenzaldehyde) in the presence glacial acetic acid as a solvent Schiff base compounds are created. Results: The prepared compounds were identified by FT-IR, 1H NMR, 13C NMR, then the antioxidant activity of the derivatives and molecular docking were studied. D

Five derivatives of thiadiazole were prepared with aldehydes and alkyl halides, compoundA: 2-amino-5-thiol-1,3,4- thiadiazole, compound B :2-(o-hydroxybenzylidine)amino-5-thiol-1,3,4-thiadiazole, compoundC: 2(2-butan-lidine)amino-5-thiol-1,3,4-thiadiazole, compound E: 2- amino-5-(2-Propanylthio)-1,3,4-thiadiazol) and compound F:2(o-chlorobenzylamino)-5-(2-propanyl thio)-1,3,4 thiadiazol. All prepared compounds were diagnosed by (IR) and (UV) Spectroscopy. All of those compounds were screened for their anti-microbial activity in vitro. The results show that most of the compounds A, B, C exhibited moderate to good activity against Gram-positive bacteria and the same compound exhibit low to moderate activity on most gram-negative bacte

The compounds 3-[4̄-(4˭-methoxybenzoyloxy) benzylideneamino]-2-thioxo-imidazolidine-4-one(3)aand 4-(1-(5-oxo- 2-thioxoimidazolidin-1-ylimino)ethyl)phenyl acetate(3)b were prepared from the reaction of aromatic aldehyde or ketone(1)a,bwith thiosemicarbazide to give aryl thiosemicarbazones(2)a,b ,followed by cyclization with ethylchloroacetate in the presence of fused sodium acetate. Treatment the compounds(3)a,bwith 4- hydroxybenzenediazoniumchloride yielded the correspondings4-((4-((4-hydroxyphenyl)diazenyl)-5-oxo-2- thioxoimidazolidin-1-ylimino)methyl)phenyl 4-methoxybenzoate(4)aand4-(1-(4-((4-hydroxyphenyl)diazenyl)-5-oxo-2- thioxoimidazolidin-1-ylimino)ethyl)phenyl acetate(4)b.The new 2-thioxo-imidazolidin-4-one with esters (5-7)a,b sy