On complex fractal-fractional order mathematical modeling of CO ₂ emanations from energy sector

Abstract

This research work is devoted to undertake a mathematical model for emissions of carbon dioxide (CO 2) from energy sector using the concept of fractals-fractional differential (FFD) operator. Here, it should be kept in mind that as the population is expanding, so the need of energy increasing day by day. Burning fossil fuels accounts for a sizable amount of the world’s energy production, which increases the concentration of CO 2 in the atmosphere and causes the global warming. It’s critical to reduce CO 2 emissions from the energy industry. Therefore, via the use of FFD operator, we investigate a mathematical model which is addressing the mentioned process. We deduce some qualitative results regarding the existence of such models in real life using mathematical analysis. The aforesaid analysis is based on some fixed points approaches. Additionally, some analysis devoted to stability is also derived for the proposed model. In addition, a numerical algorithms based on modified Euler method is constructed to simulate the results graphically.

Analysis of fractal-fractional Alzheimer's disease mathematical model in sense of Caputo derivative

“…The fractal fractional derivation is suitable for describing systems with temporal memory and a wide range of spatial influences. Several significant findings have emerged from the application of fractal-fractional operators to solve diverse models in the fields of biology [40] , [42] and physics [41] , [43] . This emerging field of study has demonstrated its efficacy in tackling complex problems and is poised to make significant contributions to various scientific disciplines [32] – [35] .…”

On mathematical model of infectious disease by using fractals fractional analysis

“…Additionally, the numerical investigation for various fractals fractional orders will be performed by using the aforementioned numerical scheme. The aforesaid numerical scheme has been used very well for other problems of fractals fractional derivatives; we refer to [28], [42]. Here, it is important to mention that we use the fixed point approach [9] which was also used to study a fractals fractional order model by authors [2].…”