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On a robust stability criterion in the Cattaneo–Hristov diffusion equation


             [6] Khajanchi S., Sardar M. & Nieto J. (2023). Ap-   Frontiers in fractional calculus. Bentham Science
                plication of non-singular kernel in a tumor model  Publishers, Sharjah, 269–341.
                with strong allee effect. Differential Equations  [17] Hristov J. (2019). Response functions in lin-
                and Dynamical Systems 31(1), 687–692. https:      ear  viscoelastic  constitutive  equations  and
                //doi.org/10.1007/s12591-022-00622-x              related  fractional  operators.  Mathematical
             [7] Sehra, H. Sadia, S. Haq, H. Alhazmi, I. Khan     Modelling of Natural Phenomena 14(3), 305.
                & Niazai S. (2004). A comparative analysis of     https://doi.org/10.1051/mmnp/2018067
                three distinct fractional derivatives for a second  [18] Hristov  J.  (2023).  Constitutive  fractional
                grade fluid with heat generation and chemical     modeling.  Mathematical  Modelling:   Prin-
                reaction. Scientific Reports 14(1), 4482. https:  ciple And Theory. 786,    37–140. h t t p s :
                //doi.org/10.1038/s41598-024-55059-9              //doi.org/10.1090/conm/786/15795
             [8] Caputo M. & Fabrizio M. (2015). A new defini-  [19] Hristov J. (2023). The fading memory formalism
                tion of fractional derivative without singular ker-  with Mittag–Leffler-type kernels as a generator
                nel. Progress in Fractional Differentiation & Ap-  of non-local operators. Applied Sciences 13(5),
                plications 1(2), 73–85.                           3065. https://doi.org/10.3390/app13053065
             [9] Atangana A. & Baleanu D. (2016). New frac-   [20] Koka  I.  &   Atangana  A.   (2017).  Solu-
                tional derivatives with nonlocal and non-singular  tions  of  Cattaneo–Hristov  model  of  elas-
                kernel: Theory and application to heat transfer   tic  heat   diffusion  with  Caputo–Fabrizio
                model. Thermal Science 20(2), 763–769. https:     and   Atangana–Baleanu    fractional  deriva-
                //doi.org/10.2298/TSCI160111018A                  tives.  Thermal  Science  21(6A),  2299–2305.
            [10] Tateishi A., Ribeiro H. & Lenzi E. (2017). The   https://doi.org/10.2298/TSCI160209103K
                role of fractional time-derivative operators on  [21] Sene N. (2019). Solutions of fractional diffu-
                anomalous diffusion. Frontiers in Physics 5, 52.  sion equations and Cattaneo–Hristov diffusion
                https://doi.org/10.3389/fphy.2017.00052           model.  International  Journal  of  Analysis
            [11] Vivas-Cruz L., Gonz´alez-Calder´on A., Taneco-   and Applications 17(2),  191–207. h t t p s :
                Hern´andez M. & Luis D. (2020). Theoretical anal-  //doi.org/10.28924/2291-8639-17-2019-191
                                                                                       ˙
                ysis of a model of fluid flow in a reservoir with  [22] Avcı D. & Ero˘glu B. B. I. (2021) Optimal control
                the Caputo–Fabrizio operator. Communications      of the Cattaneo–Hristov heat diffusion model.
                in Nonlinear Science and Numerical Simulation     Acta Mechanica 232(9) 3529–3538. h t t p s :
                84, 105186. https://doi.org/10.1016/j.cnsn        //doi.org/10.1007/s00707-021-03019-z
                                                                                ˙
                s.2020.105186                                 [23] Ero˘glu B. B. I. & Avcı  D. (2021). Separa-
            [12] Sene N. & Ndiaye A. (2024). Existence and        ble solutions of Cattaneo–Hristov heat dif-
                uniqueness study for partial neutral functional   fusion equation in a line segment:  Cauchy
                fractional differential equation under Caputo     and   source  problems.   Alexandria  Engi-
                derivative. An International Journal of Opti-     neering Journal 60(2), 2347–2353. h t t p s :
                mization and Control: Theories & Applications     //doi.org/10.1016/j.aej.2020.12.018
                (IJOCTA), 14(3), 208–219. https://doi.org/    [24] Singh Y., Kumar D., Modi K. & Gill V. (2020). A
                10.11121/ijocta.1464                              new approach to solve Cattaneo–Hristov diffusion
            [13] Hristov J. (2013). A note on the integral approach  model and fractional diffusion equations with
                to non-linear heat conduction with Jeffrey’s fad-  Hilfer–Prabhakar derivative. AIMS Mathematics
                ing memory. Thermal Science, 17(3), 733–737.      5(2), 843–855.
                                                                                  ˙
                https://doi.org/10.2298/TSCI120826076H        [25] Ero˘glu  B.  B.  I.  (2023).  Two-dimensional
            [14] Hristov J. (2016). Transient heat diffusion      Cattaneo–Hristov heat diffusion in the half-
                with a non-singular fading memory: From the       plane. Mathematical Modelling and Numerical
                Cattaneo constitutive equation with Jeffrey’s     Simulation with Applications. 3(3), 281–296.
                Kernel to the Caputo–Fabrizio time-fractional     https://doi.org/10.53391/mmnsa.1340302
                derivative. Thermal Science, 20(1), 757–762.  [26] Elsgolts L. (1997). Differential equations and the
                https://doi.org/10.2298/TSCI160112019H            calculus of variations, Mir, Moscow.
            [15] Hristov  J.  (2017).  Steady-state  heat  con-  [27] Brezis  H.  (2011).  Functional  analysis,
                duction  in  a  medium   with  spatial  non-      Sobolev   spaces  and    partial  differential
                singular  fading  memory:     derivation  of      equations,  Springer,  New  York.  h t t p s :
                Caputo–Fabrizio   space-fractional  derivative    //doi.org/10.1007/978-0-387-70914-7
                with   Jeffrey’s  kernel  and  analytical  so-
                                                              [28] Kilbas A., Srivastava H. & Trujillo J. (2006).
                lutions.  Thermal  Science,  21(2),  827–839.
                                                                  Theory and applications of fractional differential
                https://doi.org/10.2298/TSCI160229115H
                                                                  equations, Elsevier Science Inc., USA.
            [16] Hristov J. (2018). Derivatives with non-singular
                kernels from the Caputo–Fabrizio definition   [29] Losada J. & Nieto J. (2015). Properties of
                and beyond: Appraising analysis with emphasis     a new fractional derivative without singular
                on diffusion models. In: Sachin Bhalekar, ed.     kernel. Progress in Fractional Differentiation &
                Current developments in mathematical sciences.    Applications 1(2), 87–92.

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