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<p>Mitochondrial calcium-dissociation gathers inside the mitochondria of vascular soft tissue cells and is able to interrupt phosphate resolution for up to an hour. In this study, we study the fractional model of mitochondrial calcium-phosphate dissolution (MCD) a system utilizing the Caputo-Fabrizio operator equipped by order <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1918_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>. Furthermore, the theory of the existence of solutions is demonstrated to ensure there exists at least single solution to the considered model. The Picard-Lindelof approach and Banach fixed point theorem are adopted to explore the existence of the solution of the proposed model. Additionally, numerical outcomes of the system are achieved by the three-step Adams-Bashforth method. Graphs of approximate solutions are simulated to show complex behavior of the mitochondrial calcium-dissociation model for a few fractional orders and initial conditions. Some theoretical results of the robust control are obtained to control chaos dynamics.</p>

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Investigating Mitochondrial Calcium-Phosphate Dissolution Fractional Order System with Robust Control

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Mohammad Partohaghighi,
  • Shabir Ahmad,
  • Tayyaba Akram

摘要

Mitochondrial calcium-dissociation gathers inside the mitochondria of vascular soft tissue cells and is able to interrupt phosphate resolution for up to an hour. In this study, we study the fractional model of mitochondrial calcium-phosphate dissolution (MCD) a system utilizing the Caputo-Fabrizio operator equipped by order \(\alpha \) α . Furthermore, the theory of the existence of solutions is demonstrated to ensure there exists at least single solution to the considered model. The Picard-Lindelof approach and Banach fixed point theorem are adopted to explore the existence of the solution of the proposed model. Additionally, numerical outcomes of the system are achieved by the three-step Adams-Bashforth method. Graphs of approximate solutions are simulated to show complex behavior of the mitochondrial calcium-dissociation model for a few fractional orders and initial conditions. Some theoretical results of the robust control are obtained to control chaos dynamics.