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Fractional Order Mathematical Modelling for Studying the Impact on the Emergence of Pollution and Biodiversity Pertaining to Incomplete Aleph Functions |
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PP: 15-22 |
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doi:10.18576/pfda/100102
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Author(s) |
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Shaher Momani,
Rahul Sharma,
Jagdev Singh,
Yudhveer Singh,
Samir Hadid,
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Abstract |
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| Civilizations are always known for utilization, destruction and ignoring the environment. Different opinions have been put at the root of our environmental-disruptive tendencies, religion, social and economic structures and the adoption of technology. It is conventional to blame environmental conditions but we do not utilize practically our knowledge and understanding of nature. It seems that we continuously blame pollution and its destruction instead of our efforts. With the use of a fractional order mathematical model involving incomplete Aleph (א) functions (IAFs) and the Caputo fractional derivative, we explore the impact of the emergence of pollution and study the effect of industrial operations on the environment of the region. In this work, we evaluate the Caputo fractional derivative of incomplete Aleph (א) functions. Here, we define the concentration C(x,t) in terms of incomplete Aleph (א) functions and obtain some particular cases by giving specific values to the parameters of our primary results and expressing them in terms of special functions, notably H-functions, incomplete H-functions, and incomplete I-functions, and demonstrating their relationship with existing results.
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