Analysis of a class of fractal hybrid fractional differential equation with application to a biological model

Thabet Abdeljawad, Muhammad Sher, Kamal Shah, Muhammad Sarwar, Inas Amacha*, Manar Alqudah, Asma Al-Jaser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Recently, the area devoted to fractional calculus has given much attention by researchers. The reason behind such huge attention is the significant applications of the mentioned area in various disciplines. Different problems of real world processes have been investigated by using the concepts of fractional calculus and important and applicable outcomes were obtained. Because, there has been a lot of interest in fractional differential equations. It is brought on by both the extensive development of fractional calculus theory and its applications. The use of linear and quadratic perturbations of nonlinear differential equations in mathematical models of a variety of real-world problems has received a lot of interest. Therefore, motivated by the mentioned importance, this research work is devoted to analyze in detailed, a class of fractal hybrid fractional differential equation under Atangana- Baleanu- Caputo ABC derivative. The qualitative theory of the problem is examined by using tools of non-linear functional analysis. The Ulam-Hyer’s (U-H) type stability criteria is also applied to the consider problem. Further, the numerical solution of the model is developed by using powerful numerical technique. Lastly, the Wazewska-Czyzewska and Lasota Model, a well-known biological model, verifies the results. Several graphical representations by using different fractals fractional orders values are presented. The detailed discussion and explanations are given at the end.

Original languageEnglish
Article number18937
JournalScientific Reports
Volume14
Issue number1
DOIs
Publication statusPublished - Dec 2024
Externally publishedYes

Keywords

  • Existence theory
  • Fractal Fractional derivative
  • Numerical results
  • U-H stability

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