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The population model has an important role in biology to interpret the spreading rate of viruses and parasites. This biological model is also used to identify fragile species. This paper aims to propose a new Yang-Abdel-Aty-Cattani (YAC) fractional operator with a non-singular kernel to solve nonlinear partial differential equation, which is arised in biological population model. Here, this study has explained the analytical methods, reduced differential transform method (RDTM) and residual power series method (RPSM) taking the fractional derivative as YAC operator sense.

This study has explained the analytical methods, RDTM and RPSM taking the fractional derivative as YAC operator sense.

This study has expressed the solutions in terms of Mittag-Leffler functions. Also, this study has compared the solutions with the exact solutions. Three examples are described for the accuracy and efficiency of the results.

The population model has an important role in biology to interpret the spreading rate of viruses and parasites. This biological model is also used to identify fragile species. In this study, the main aim is to propose a new YAC fractional operator with non-singular kernel to solve nonlinear partial differential equation, which is arised in biological population model. Here, this study has explained the analytical methods, RDTM and RPSM taking the fractional derivative as YAC operator sense. This study has expressed the solutions in terms of Mittag-Leer functions. Also, this study has compared the solutions with the exact solutions. Three examples are described for the accuracy and efficiency of the results.

The population model has an important role in biology to interpret the spreading rate of viruses and parasites. This biological model is also used to identify fragile species. In this paper, the main aim is to propose a new YAC fractional operator with non-singular kernel to solve nonlinear partial differential equation which is arised in biological population model. Here, this study has explained the analytical methods, RDTM and RPSM taking the fractional derivative as YAC operator sense. This study has expressed the solutions in terms of Mittag-Leer functions. Also, this study has compared the solutions with the exact solutions. Three examples are described for the accuracy and efficiency of the results.

The population model has an important role in biology to interpret the spreading rate of viruses and parasites. This biological model is also used to identify fragile species. In this paper, the main aim is to propose a new YAC fractional operator with non-singular kernel to solve nonlinear partial differential equation, which is arised in biological population model. Here, this paper has explained the analytical methods, RDTM and RPSM taking the fractional derivative as YAC operator sense. This study has expressed the solutions in terms of Mittag-Leer functions. Also, this study has compared the solutions with the exact solutions. Three examples are described for the accuracy and efficiency of the results.

The population model has an important role in biology to interpret the spreading rate of viruses and parasites. This biological model is also used to identify fragile species. In this paper, the main aim is to propose a new YAC fractional operator with non-singular kernel to solve nonlinear partial differential equation, which is arised in biological population model. Here, this paper has explained the analytical methods, RDTM and RPSM taking the fractional derivative as YAC operator sense. This study has expressed the solutions in terms of Mittag-Leer functions. Also, this study has compared the solutions with the exact solutions. Three examples are described for the accuracy and efficiency of the results.

The purpose of this paper is to analytically solve the (2+1)-dimensional nonlinear time fractional biological population model in the Caputo sense.

The paper uses the variable separation method and the properties of Gamma function to construct exact solutions of the time fractional biological population model.

New variable separation solutions are obtained, from which some known solutions are recovered as special cases.

Solving fractional biological population model by the variable separation method and the properties of Gamma function is original. It is shown that the method presented in this paper can be also used for some other nonlinear fractional partial differential equations arising in sciences and engineering.

Investigation of the smoking model is important as it has a direct effect on human health. This paper focuses on the numerical analysis of the fractional order giving up smoking model. Nonetheless, due to observational or experimental errors, or any other circumstance, it may contain some incomplete information. Fuzzy sets can be used to deal with uncertainty. Yet, there may be some inconsistency in the membership as well. As a result, the primary goal of this proposed work is to numerically solve the model in a type-2 fuzzy environment.

Triangular perfect quasi type-2 fuzzy numbers (TPQT2FNs) are used to deal with the uncertainty in the model. In this work, concepts of r2-cut at r1-plane are used to model the problem's uncertain parameter. The Legendre wavelet method (LWM) is then utilised to solve the giving up smoking model in a type-2 fuzzy environment.

LWM has been effectively employed in conjunction with the r2-cut at r1-plane notion of type-2 fuzzy sets to solve the model. The LWM has the advantage of converting the non-linear fractional order model into a set of non-linear algebraic equations. LWM scheme solutions are found to be well agreed with RK4 scheme solutions. The existence and uniqueness of the model's solution have also been demonstrated.

To deal with the uncertainty, type-2 fuzzy numbers are used. The use of LWM in a type-2 fuzzy uncertain environment to achieve the model's required solutions is quite fascinating, and this is the key focus of this work.

In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).

The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM).

The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations.

The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature.

Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space‐time configurations. No one has tried to analyze a generative power of cellular‐automaton machines. The purpose of this paper is to fill the gap and develop a basis for future studies in generative complexity of large‐scale spatially extended systems.

Let all but one cell be in alike state in initial configuration of a one‐dimensional cellular automaton. A generative morphological diversity of the cellular automaton is a number of different three‐by‐three cell blocks occurred in the automaton's space‐time configuration.

The paper builds a hierarchy of generative diversity of one‐dimensional cellular automata with binary cell‐states and ternary neighborhoods, discusses necessary conditions for a cell‐state transition rule to be on top of the hierarchy, and studies stability of the hierarchy to initial conditions.

The method developed will be used – in conjunction with other complexity measures – to built a complete complexity maps of one‐ and two‐dimensional cellular automata, and to select and breed local transition functions with highest degree of generative morphological complexity.

The hierarchy built presents the first ever approach to formally characterize generative potential of cellular automata.

New Public Management (NPM)-style reforms have resulted in unintended effects such as fragmentation, deficient coordination and undermining political control. This book is in search of new steering concepts to counter this fragmentation and re-coordinate the public sector. In this chapter, the search for new steering concepts is addressed by looking at a type of public management reform that is an extremely ‘wicked problem’ in terms of steering and coordination, that is, emergent and complex change processes. Such a type of reform process is a complex network of different sub-types of reform with a multitude of actors with different interests and motives. Many decentral actors initiate various reforms at different places from which in the course of time a trend emerges, and several central actors try to coordinate and supervise, but have limited influence. Such an ‘emergent and complex’ type of change process indeed requires fundamentally new steering concepts.

The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.

The trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.

The profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.

Moreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.

In a world characterised by increasing environmental and social awareness, the number of corporate social responsibility and sustainability initiatives has significantly grown. Among these, the United Nations Global Compact (UNGC) is one of the most important, involving more than 12,000 companies. The purpose of this study is to investigate the UNGC’s worldwide diffusion, both at country and industry level, to understand the reasons leading to the highlighted dissemination patterns, and to propose various future projections.

The study pursues its objectives by applying the logistic curve model to data provided by the United Nations. The analysis is complemented by adopting instability and concentration indexes.

Results suggest that, while human rights and environmental safeguard in some areas and industries will remain a controversial issue, UNGC adoption will continue growing and giving the participants the required legitimacy to compete in worldwide markets.

To the best of the authors’ knowledge, this is the first paper that analyses the UNGC’s worldwide diffusion and proposes a prediction model for its future dissemination. The findings are of considerable importance in extending the knowledge of the initiative and in understanding the potential values of its adoption.

Our physical universe is 1.5×10¹⁰ years old. It began with the Big Bang. There is some debate about what happened in the first tenth of a second! The first 3×10⁵ years were radiation dominated. Since then it has been matter dominated. (This in accordance with the first law of thermodynamics which states that total mass-energy is conserved.) The universe has continuously expanded in space and in the future either this may continue, or expansion may stabilise at a fixed size or the universe may contract in the Big Crunch (depending on the spatial curvature). At a certain scale the universe is spatially isotropic and homogeneous. Its trajectory exhibits increasing entropy in accordance with the second law of thermodynamics. These statements are in accordance with certain models and empirical data: distant galaxies are receding from us at a velocity proportional to their distance; there is greater spatial uniformity at greater distances from us; there is uniform presence in space of radiation with a temperature of 2.7K; etc.

The decomposition method is used for solving differential systems in biology and medicine. A comparison is given between the Runge‐Kutta method and the decomposition technique. New relationships for calculating Adomian’s polynomials are used for solving the differential systems governing the competition between species and based on the Lotka‐Volterra model.