4‐Cyano‐5,6‐diphenyl‐2,3‐dihydropyridazine‐3‐onc 1 reacts with phosphorous oxychloride to give 70% of the corresponding 3‐chloro derivative 2. Treating 2 with anthranilic acid in butanol, 4‐cyano‐2,3‐diphenyl‐10H‐pyridazino[6,1‐b]quinoxaline‐10‐one, 3 was obtained. Compound 1 reacts with phosphorous pentasulphide to give 3‐mercapto derivative 4, which was converted by acrylonitrile to S‐(2‐cyanoethyl)pyridazine derivative 5. Compound 4 reacts with ethyl bromoacetate and with phenacyl bromide gave the corresponding thieno[2,3‐c] pyridazine derivatives 8, 9, Alkylation of 1 with ethyl chloroacetate afforded 3‐0‐carbethoxymethyl derivative 10. Compound 10 reacts with amines (aniline, hydrazine) to give the corresponding amide and acid hydrazide 13, 12 respectively. Hydrolysis of 10 with sodium hydroxide gave the corresponding acid derivative 11. Treating 1 with methyl iodide, 3‐0‐methyl derivative 14 was obtained, which was converted by ammonium acetate/acetic acid to 3‐amino‐4‐cyano‐5,6‐diphenyl pyridazine 15. Compound 1 reacts with methyl magnesium iodide gave 4‐acetyl derivative 16, which was reacted with hydrazine, phenyl hydrazine and with hydroxylamine to give the substituted I H pyrazolo [3,4‐c] pyridazine 17 a,b and isoxazolo [5,4‐c] pyridazine 18 derivatives respectively.
The Kaup–Newell equation is used to model sub-picoseconds pulses that travel throughout optical fibers. The fractional-order perturbed Kaup–Newell model, which represents extensive waves parallel to the field of magnetic, is examined. In this paper, two analytical techniques named, improved F-expansion and generalized exp[Formula: see text]-expansion techniques, are employed and new analytical solutions in generalized forms like bright solitons, dark solitons, multi-peak solitons, peakon solitons, periodic solitons and further wave results are assembled. These soliton solutions and other waves findings have important applications in applied sciences. The configurations of some solutions are shown in the form of graphs through assigning precise values to parameters, and their dynamics are described. The illustrated novel structures of some solutions also assist engineers and scientists in better grasping the physical phenomena of this fractional model. A comparison analysis has been given to explain the originality of the current findings compared to the previously achieved results. The results of computer simulations show that the procedures described are effective, simple, and efficient.
In modern world, most of the optimization problems are nonconvex which are neither convex nor concave. The objective of this research is to study a class of nonconvex functions, namely, strongly nonconvex functions. We establish inequalities of Hermite-Hadamard and Fejér type for strongly nonconvex functions in generalized sense. Moreover, we establish some fractional integral inequalities for strongly nonconvex functions in generalized sense in the setting of Riemann-Liouville integral operators.
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