In this paper, a fixed point theorem of nonexpansive mapping is established to study the existence and sufficient conditions for the controllability of nonlinear fractional control systems in reflexive Banach spaces. The result so obtained have been modified and developed in arbitrary space having Opial’s condition by using fixed point theorem deals with nonexpansive mapping defined on a set has normal structure. An application is provided to show the effectiveness of the obtained result.

This article introduces a novel procedure to detect an approximate solution to Fredholm fractional integro-differential equations with linear type (LFFIDE) defined using Caputo fractional derivative. The new procedure approximates the solution using three types of polynomials: Laguerre polynomials, Hermite polynomials, and Legendre polynomials, thereafter transforming the problem into a linear programming problem. The approximate solutions are compared using testing examples to examine the efficiency of the suggested approach. Also, a comparison with the other methods using the same polynomials illustrates The effectiveness and consistency of the proposed technique. Finally, the error analysis of the proposed technique and convergent are di

Azo derivative ligand[H3L] have been synthesized by the reaction of diazonium salt of p-amino benzoic acid with orcinol in(1:1)mole ratio. The bidente ligand was reacted with the metal ions MnII,FeIIandCrIIIin(2:1)mole ratio via reflux in ethanol using Et3N as a base to give complexes of the general formula: [ M(H2L)2(H2O)x]Cly The synthesized compounds were characterized by spectroscopic methods[ I.R , UV-Vis, A.A and H1 NMR]along with melting point, chloride content and conductivity measurements. The complexes were screend for their in vitro antibacterial activity against one strain of staphylococcus as Gram(+) positive and one strain of pseudomonas as Gram(-) Negative, using the agar diffusion technique.

Synthesis and biological studies 0fCo(||)،Ni(||)،Cu(||) And Zn(||)complexes with New compound N-(2,3-dioxoindolin-1-yl)_N_methyl benzamide

The 3-aminoacetophenone and 4-aminoantipyrine were used as ‎precursors to prepare new six ligands. The three new ligands (L1,L2 ‎and L3) were synthesis by reacting one mole of 3-aminoacetophenone ‎with one mole of (Acetyl chloride), (benzoyl chloride), (4-‎methoxybenzoyl chloride) and ammonium thiocyanat in acetone as a ‎solvent, they are:-‎ L1 (AAA) =[N-(3-acetylphenylcarbamothioyl)acetamide]‎ L2 (BAA) =[N-(3-acetylphenylcarbamothioyl)benzamide]‎ L3 (MAA) =[N-(3-acetylphenylcarbamothioyl)-4-methoxy benzamide]‎ Also three new derivatives of 4-aminoantipyrine were synthesis by ‎reacting one mole of 4-aminoantipyrine with one mole of (Acetyl ‎chloride), (benzoyl chloride), (4-methoxybenzoyl chloride) and ‎ammonium thio