This work evaluates the fractional complex Ginzburg-Landau equation in the sense of truncated M- fractional derivative and analyzes its soliton solutions and other new solutions in the appearance of a detuning factor in non-linear optics. The multiple, bright, and bright-dark soliton solutions of this equation are obtained using the modified $\left(G^{\prime }/G^2\right)$ and $\left(1/G^{\prime }\right)-$expansion methods. The equation is evaluated with Kerr law, quadratic –cubic law and parabolic law non-linear fibers. To shed light on the behavior of solitons, the graphical illustrations in the form of 2D and 3D of the obtained solutions are represented for different values of various parameters. All of the solutions have been verified by substitution into their corresponding equations with the aid of a symbolic software package. The various forms of solutions to the aforementioned nonlinear equation that arises in fluid dynamics and nonlinear processes are presented. Moreover, we guarantee that all the solutions are new and an excellent contribution in the existing literature of solitary wave theory.

The evaluation of compact heat density gadgets requires effective measures for heat transportation. Enhancement in thermal transportation of hybrid nanofluids comprising of water plus ethyl glycol with the dispersion of three different nano-entities is considered. The fluids are transported through a porous medium over a permeable elongating sheet. Water and ethyl glycol are $(50\mathrm{\%}-50\mathrm{\%})$. The three cases for hybrid species consist of (a) Graphene oxide (Go) + AA7072, (b) Go + Molybdenum sulfide, (c) Go + silver. The volume fraction of nano-entities is greater than 0.3%. It is presumed that the fluid flow is non-Newtonian. Two on-Newtonian fluids models namely Maxwell fluid and Casson fluid are taken into consideration to present comparative behavior in the existence of the nano-particle mixture. The leading equations are altered into ordinary differential form. A robust numerical procedure embraced with Runge-Kutta methodology and shooting strategy is employed to attain results for the dependent physical quantities. It is noticed that the velocity is diminished against the magnetic field parameter and porosity parameter. The temperature for case (a) Go + AA7072 is the highest and it is lowest for case (c) Go + silver. The temperature and velocity functions of both the fluids (Casson and Maxwell fluids) are incremented with larger inputs of hybrid nano-species. The results can find applications for the better performance of electronic equipment, and heat exchangers.