A comparative analysis of plasma dilution based on fractional integro-differential equation: an application to biological science

References

• Hahn RG, Warner DS. Volume kinetics for infusion fluids. Anesthesiology. 2010;113(2):470–481.
   PubMed Web of Science ®Google Scholar
• Brandstrup B, Tønnesen H, Beier-Holgersen R. Effects of intravenous fluid restriction on postoperative complications: comparison of two perioperative fluid regimens: a randomized assessor-blinded multicenter trial. Ann Surg. 2003;238(5):641–648.
   PubMed Web of Science ®Google Scholar
• Som A, Maitra S, Bhattacharjee S, et al. Goal directed fluid therapy decreases postoperative morbidity but not mortality in major non-cardiac surgery: a meta-analysis and trial sequential analysis of randomized controlled trials. J Anesth. 2017;31(1):66–81.
   PubMed Web of Science ®Google Scholar
• Marik PE, Baram M, Vahid B. Does central venous pressure predict fluid responsiveness? a systematic review of the literature and the tale of seven mares. Chest. 2008;134(1):172–178.
   PubMed Web of Science ®Google Scholar
• Ali Abro K, Gómez-Aguilar JF. Dual fractional analysis of blood alcohol model via non-integer order derivatives, fractional derivatives with Mittag-Leffler kernel, studies in systems. Decis Control. 2019;194. DOI:10.1007/978-3-030-11662-0_5
   Google Scholar
• Richard C, Warszawski J, Anguel N, et al. Early use of the pulmonary artery catheter and outcomes in patients with shock and acute respiratory distress syndrome: a randomized controlled trial. JAMA. 2003;290(20):2713–2720.
   PubMed Web of Science ®Google Scholar
• Atlas G, Brealey D, Dhar S, et al. Additional hemodynamic measurements with an esophageal Doppler monitor: a preliminary report of compliance, force, kinetic energy, and afterload in the clinical setting, J Clin Monit Comput, 2012, 26, 473–482.
   Google Scholar
• Hahn RG, Svensen C. Plasma dilution and the rate of infusion of Ringer’s solution. Br J Anaesth. 1997;79(1):64–67.
   PubMed Web of Science ®Google Scholar
• Guo Z, Karen MB, Kaushik C, et al. Mathematical modeling of material-induced blood plasma coagulation. Biomaterials. 2006;27(5):796–806.
   PubMed Web of Science ®Google Scholar
• Saskia EMS, Marion AHF, Marcus DL. Effects of plasma dilution on tissue factor–induced thrombin generation and thromboelastography: partly compensating role of platelets. Transfusion. 2008;48(11):2384–2394.
   PubMed Web of Science ®Google Scholar
• Christer H, Edgaras S, Jacob B, et al. Evaluation of hydration status calculated from differences in venous and capillary plasma dilution during stepwise crystalloid infusions: a randomized crossover study in healthy volunteers. Medicina (B Aires). 2014;50(5):255–262.
   Google Scholar
• Elena IS, Alexander SG, Elena AS, et al. Moderate plasma dilution using artificial plasma expanders shifts the haemostatic balance to hypercoagulation. Sci Rep. 2017;7(1):843–855.
   PubMed Web of Science ®Google Scholar
• Liang X, Chernysh I, Purohit PK. Phase transitions during compression and decompression of clots from platelet-poor plasma, platelet-rich plasma and whole blood. Acta Biomater. 2017;60:275–290.
   PubMed Web of Science ®Google Scholar
• Ali-Abro K, Khan I, Gómez-Aguilar JF. A mathematical analysis of a circular pipe in rate type fluid via Hankel transform. Eur Phys J Plus. 2018;133(10):397.
   Web of Science ®Google Scholar
• Rashidi MM, Momoniat E, Rostami B. Analytic approximate solutions for MHD boundary-layer viscoelastic fluid flow over continuously moving stretching surface by homotopy analysis method with two auxiliary parameters. J Appl Math. 2012; Article ID 780415. 2012: 19.
   Web of Science ®Google Scholar
• Abro KA, Mukarrum H, Mirza MB. Influences of magnetic field in viscoelastic fluid. Int J Nonlinear Anal Appl. 2018;9(1):99–109.
   Google Scholar
• Rostami B, Rashidi MM, Rostami P, et al. Analytical investigation of laminar viscoelastic fluid flow over a wedge in the presence of buoyancy force effects. Abstr Appl Anal. 2014; Article ID 496254. 2014: 11.
   Google Scholar
• Muzaffar HL, Kashif AA, Asif AS. Helical flows of fractional viscoelastic fluid in a circular pipe. Int J Adv Appl Sci. 2017;4(10):97–105.
   Web of Science ®Google Scholar
• Koca I, Atangana A. Solutions of Cattaneo-Hristov model of elastic heat diffusion with Caputo-Fabrizio and atangana-baleanu fractional derivatives. Thermal Sci. 2016;21(6 Part A):2299–2305.
   Web of Science ®Google Scholar
• Ali Abro K, Gómez-Aguilar JF. A comparison of heat and mass transfer on a Walter’s-B fluid via Caputo-Fabrizio versus Atangana-Baleanu fractional derivatives using the Fox-H function. Eur Phys J Plus. 2019;134(3):101.
   Web of Science ®Google Scholar
• Bahiraei M, Hangi M. Flow and heat transfer characteristics of magnetic nanofluids: a review. J Magn Magn Mater. 2015;374:125–138.
   Web of Science ®Google Scholar
• Ali Abro K, Khan I, Gómez-Aguilar JF. Thermal effects of magnetohydrodynamic micropolar luid embedded in porous medium with Fourier sine transform technique, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2019;41:1–9. DOI:10.1007/s40430-019-1671-5
   Google Scholar
• Khan U, Khan SI, Ahmed N, et al. Heat transfer analysis for squeezing flow of a Casson fluid between parallel plates. Ain Shams Engin J. 2016;7(1):497–504.
   Web of Science ®Google Scholar
• Khan I, Abro KA, Mirbhar MN. Thermal analysis in Stokes’ second problem of nanofluid: applications in thermal engineering. Case Stud Thermal Eng. 2018 2018 Apr 10;12:271–275. Available online.
   Web of Science ®Google Scholar
• Mohyud-Din ST, Yildirim A. An algorithm for solving the fractional vibration Equation. Comput Math Model. 2012;23(2):228–236.
   Google Scholar
• Ali Abro K, Yildirim A. Fractional treatment of vibration equation through modern analogy of fractional differentiations using integral transforms. Iran J Sci Technol Transaction A. 2019;43:1–8.
   Web of Science ®Google Scholar
• Khan I. Shape effects of MoS 2 nanoparticles on MHD slip flow of molybdenum disulphide nanofluid in a porous medium. J Mol Liq. 2017;233:442–451.
   Web of Science ®Google Scholar
• Ali Abro K, Ali Abro I, Mustafa Almani S, et al. On the thermal analysis of magnetohydrodynamic Jeffery fluid via modern non integer order derivative. J King Saud Univ–Sci. 2018. DOI:10.1016/j.jksus.2018.07.012
   Web of Science ®Google Scholar
• Zafar AA, Fetecau C. Flow over an infinite plate of a viscous fluid with non-integer order derivative without singular kernel. Alexandria Eng J. 2016;55(3):2789–2796.
   Web of Science ®Google Scholar
• Ali Abro K, Hussain M, Mahmood Baig M. A mathematical analysis of magnetohydrodynamic generalized burger fluid for permeable oscillating plate. Punjab Univ J Math. 2018;50(2):97–111.
   Web of Science ®Google Scholar
• Owolabi KM, Atangana A. Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations. Chaos Solitons Fractals. 2018;111:119–127.
   Web of Science ®Google Scholar
• Ali Abro K, Asghar Memon A, Memon AA. Functionality of circuit via modern fractional differentiations. Analog Integr Circuits Signal Process. 2019;99(1):11–21.
   Web of Science ®Google Scholar
• Gómez-Aguilar JF, Atangana A. Fractional derivatives with the power-law and the Mittag-Leffler kernel applied to the nonlinear Baggs-Freedman model. Fractal Fract. 2018;2(10):1–14.
   Google Scholar
• Ali Abro K. Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators. Numer Methods Partial Differ Eq. 2020;1–15. DOI:10.1002/num.22727
   Web of Science ®Google Scholar
• Sania Q, Norodin AR, Dumitru B. New numerical aspects of Caputo-Fabrizio fractional derivative operator. Mathematics. 2019;7(4):374.
   Web of Science ®Google Scholar
• Podlubny I. Fractional differential equations. San Diego: Academic press; 1999.
   Google Scholar
• Parvaiz AN, Mehmet Y, Sania Q, et al. Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan. Eur Phys J Plus. 2020;135(10):1–42.
   Web of Science ®Google Scholar
• Mainardi F. Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models. London: Imperial College Press; 2010.
   Google Scholar
• Esra KA, Ali A, Mehmet Y. New illustrative applications of integral transforms to financial models with different fractional derivatives. Chaos Solitons Fractals. 2021;146:110877.
   Web of Science ®Google Scholar
• Mehmet Y, Tukur AS, Thabet A AY. The Schrodinger-KdV equation of fractional order with Mittag-Leffler nonsingular kernel. Alexandria Eng J. 2021;60(2):2715–2724.
   Web of Science ®Google Scholar
• Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Progr Fract Differ Appl. 2015;1:73–85.
   Google Scholar
• Mehmet Y, Ndolane S. Fundamental calculus of the fractional derivative defined with rabotnov exponential kernel and application to nonlinear dispersive wave model. J Ocean Eng Sci. 2021;6(2):196–205.
   Web of Science ®Google Scholar
• Qureshi S, Yusuf A. Modeling chickenpox disease with fractional derivatives: From Caputo to atangana-baleanu Chaos. Solitons Fractals. 2019;122:111–118. 10.1016/j.chaos.2019.03.020.
   Web of Science ®Google Scholar
• Patnaik S, Hollkamp JP, Semperlotti F. Applications of variable-order fractional operators: a review. Proc R Soc. 2020;A 476(2234):20190498.
   Google Scholar
• Atangana A, Baleanu D. Caputo-Fabrizio derivative applied to groundwater flow within confined aquifer. J Eng Mech. 2016. DOI:10.1061/(ASCE)EM.1943-7889.0001091
   Web of Science ®Google Scholar
• Ambreen S, Kashif AA, Muhammad AS. Thermodynamics of magnetohydrodynamic Brinkman fluid in porous medium: Applications to thermal science. J Therm Anal Calorim. 2018;135(5):2647–2653.
   PubMed Web of Science ®Google Scholar
• Tarasov VE. No non-locality. No fractional derivative. Comm Nonlinear Sci Numer Simulat. 2018;62:157–163.
   Web of Science ®Google Scholar
• Atangana A, Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Therm Sci. 2016;20(2):763–769.
   Web of Science ®Google Scholar
• Mehmet Y. European option pricing models described by fractional operators with classical and generalized Mittag-Leffler kernels. Numer Methods Partial Differ Equations. 2021. DOI:10.1002/num.22645
   Web of Science ®Google Scholar
• J-f G-A, Torres Y-MH, Baleanu D, et al. Fractional Liénard type model of a pipeline within the fractional derivative without singular kernel. Adv Difference Equ. 2016;1:1–13.
   Google Scholar
• Samko SG. Fractional integration and differentiation of variable order. Anal Math. 1995;21(3):213–236.
   Google Scholar
• El-Nabulsi AR. The fractional calculus of variations from extended Erdélyi-Kober operator. Int J Modern Phys B. 2009;23(16):3349–3361.
   Web of Science ®Google Scholar
• Ali Abro K, Hussain M, Baig MM. An analytic study of molybdenum disulfide nanofluids using modern approach of atangana-baleanu fractional derivatives, European physical journal plus. Eur Phys J Plus. 2017; 132: 439. 2017. DOI: 10.1140/epjp/i2017-11689-y
   Web of Science ®Google Scholar
• Kottakkaran SN, Gauhar R, Khaled M. Chebyshev type inequalities via generalized fractional conformable integrals. J Comp Appl Math. 2019;346:378–389.
   Web of Science ®Google Scholar
• Doungmo Goufo EF, Atangana A. Analytical and numerical schemes for a derivative with filtering property and no singular kernel with applications to diffusion. Eur Phys J Plus. 2016;131(8):269.
   Web of Science ®Google Scholar
• El-Nabulsi RA. Fractional Dirac operators and deformed field theory on Clifford algebra. Chaos Solitons Fractals. 2009;42(5):2614–2622.
   Web of Science ®Google Scholar
• Atangana A, Gómez-Aguilar JF. Decolonisation of fractional calculus rules: breaking commutativity and associativity to capture more natural phenomena. Eur Phys J Plus. 2018;133(4):166.
   Web of Science ®Google Scholar
• Rami ENA. Fractional variational problems from extended exponentially fractional integral. Appl Math Comput. 2011;217(22):9492–9496.
   Web of Science ®Google Scholar
• Bastos NRO. Calculus of variations involving Caputo-Fabrizio fractional differentiation. Stat Optim Inf Comput. 2018;6(1):12–21.
   Google Scholar
• Atangana A. Non-validity of index law in fractional calculus: a fractional dif- ferential operator with markovian and non-markovian properties. Phys A. 2018;505:688–706.
   Web of Science ®Google Scholar
• Atangana A, Gómez-Aguilar JF. Fractional derivatives with no-index law property: application to chaos and statistics. Chaos Solitons Fractals. 2018;114:516–535.
   Web of Science ®Google Scholar
• Wang J, Dong X, Zhou Y, XiWang Dong, Yong Zhou. Analysis of nonlinear integral equations with Erdelyi-Kober fractional operator. Comm Nonl Sci Num Sim. 2012;17(8):3129–3139.
   Web of Science ®Google Scholar
• Ali Abro K, Gómez-Aguilar JF. Fractional modeling of fin on non-Fourier heat conduction via modern fractional differential operators. Arab J Sci Eng. 2021. DOI:10.1007/s13369-020-05243-6
   Web of Science ®Google Scholar
• Saima N, Shahid M, Thabet A. Fractional calculus of generalized Lommel-Wright function and its extended Beta transform. Int Transf Spec Func. 2000;9:185–196.
   Google Scholar
• Dorrego GA. Generalized Riemann-Liouville fractional operators associated with a generalization of the Prabhakar integral operator. Progr Fract Differ Appl. 2016;2(131–140):131–140.
   Google Scholar
• Roberto G, Roberto G. The Prabhakar or three parameter Mittag-Leffler function: theory and application. Commun Nonlinear Sci Numer Simulat. 2018;36:314–329.
   Google Scholar
• Garra R, Gorenflo R, Polito F, et al. Hilfer-Prabhakar derivative and some applications. Appl Math Comput. 2014;242:576–589.
   Google Scholar
• Grinko AP. Fractional type integral operators with Kummer’s confluent hypergeometric function in the kernel. Tr Inst Mat. 2011;19(1):22–31.
   Google Scholar
• Edmundo CO, José ATM. A review of definitions of fractional derivatives and other operators. Journal of Computational Physics. 2019;388:195–208.
   Google Scholar
• Srivastava HM, Harjule P, Jain R. A general fractional differential equation associated with an integral operator with the H-function in the kernel. Russian J Math Phys. 2015;22(112–126):112–126.
   Web of Science ®Google Scholar
• Vanterler J S, Capelas O E. Two new fractional derivatives of variable order with non-singular kernel and fractional differential equation. Comp Appl Math. 2018;37(4):5375–5394.
   Web of Science ®Google Scholar
• Drobin D, Hahn RG. Kinetics of isotonic and hypertonic plasma volume expanders. Anesthesiology. 2002;96(6):1371–1380.
   PubMed Web of Science ®Google Scholar
• Glen A, John KL, Shawn A, et al. Development and retrospective clinical assessment of a patient-specific closed-form integro-differential equation model of plasma dilution. Biomed Eng Comput Biol. 2017;8:1–20.
   Web of Science ®Google Scholar
• Abro KA, Atangana A, Gómez‑Aguilar JF. Role of bi‑order Atangana–Aguilar fractional differentiation on Drude model: an analytic study for distinct sources. Opt Quantum Electron. 2021;53(4):177.
   Web of Science ®Google Scholar
• Abro KA, Atangana A. A computational technique for thermal analysis in coaxial cylinder of one-dimensional flow of fractional Oldroyd-B nanofluid. Int J Ambient Energy. 2021;1–9. DOI:10.1080/01430750.2021.1939157
   Web of Science ®Google Scholar