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Bokhari, Ahmed, Baleanu, Dumitru, Belgacem, Rachid. (1401). Regularized Prabhakar derivative for partial differential equations. سامانه مدیریت نشریات علمی, 10(3), 726-737. doi: 10.22034/cmde.2021.39677.1736
Ahmed Bokhari; Dumitru Baleanu; Rachid Belgacem. "Regularized Prabhakar derivative for partial differential equations". سامانه مدیریت نشریات علمی, 10, 3, 1401, 726-737. doi: 10.22034/cmde.2021.39677.1736
Bokhari, Ahmed, Baleanu, Dumitru, Belgacem, Rachid. (1401). 'Regularized Prabhakar derivative for partial differential equations', سامانه مدیریت نشریات علمی, 10(3), pp. 726-737. doi: 10.22034/cmde.2021.39677.1736
Bokhari, Ahmed, Baleanu, Dumitru, Belgacem, Rachid. Regularized Prabhakar derivative for partial differential equations. سامانه مدیریت نشریات علمی, 1401; 10(3): 726-737. doi: 10.22034/cmde.2021.39677.1736

Regularized Prabhakar derivative for partial differential equations

Computational Methods for Differential Equations
مقاله 12، دوره 10، شماره 3، مهر 2022، صفحه 726-737    اصل مقاله (345.44 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.39677.1736
نویسندگان
Ahmed Bokhari* 1، 2؛ Dumitru Baleanu3، 4؛ Rachid Belgacem1، 2
1Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University of Chlef, Algeria.
2Laboratory of Mathematics and its Applications (LMA).
3Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, TR-06530 Ankara, Turkey.
4Institute of Space Sciences, Magurele-Bucharest, Romania.
چکیده
Prabhakar fractional operator was applied recently for studying the dynamics of complex systems from several branches of sciences and engineering. In this manuscript, we discuss the regularized Prabhakar derivative applied to fractional partial differential equations using the Sumudu homotopy analysis method(PSHAM). Three illustrative examples are investigated to confirm our main results.
کلیدواژه‌ها
Regularized Prabhakar derivative؛ Homotopy analysis method؛ Sumudu transform؛ Mittag-Leffler function
مراجع
  • [1]         O. P. Agrawal, Fractional optimal control of a distributed system using eigenfunctions, ASME. J. Comput. Non- linear Dyn, 3 (2008), 021204.
  • [2]         F. A. Aliev, N .A. Aliev, M. M. Mutallimov, and A. A. Namazov, Algorithm for Solving the Identification Problem for Determining the Fractional-Order Derivative of an Oscillatory System, Applied and computational mathematics, 19(3) (2020), 415-422.
  • [3]         B. Alkahtani, V. Gulati, A. Klman, Application of Sumudu transform in generalized fractional reaction–diffusion equation, Int. J. Appl. Comput. Math, 2 (2016), 387–394.
  • [4]         D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus: Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing, Boston, Mass, USA, 2012.
  • [5]         F. B. M. Belgacem and A. A. Karaballi, Sumudu transform fundamental properties investigations and applications, Journal of Applied Mathematics and Stochastic Analysis, (2006), 1-23
  • [6]         F. B. M. Belgacem, A. A. Karaballi, and S. L. Kalla, Analytical investigations of the Sumudu transform and applications to integral production equations, Mathematical Problems in Engineering, (2003), 103–118.
  • [7]         R. Belgacem, A. Bokhari, and B. Sadaoui, Shehu Transform of Hilfer-Prabhakar Fractional Derivatives and Applications on some Cauchy Type Problems, Advances in the Theory of Nonlinear Analysis and its Applications, 5(2) (2021), 203-214.
  • [8]         M. Caputo, Linear model of dissipation whose Q is almost frequency independent-II, Geophysical Journal of the Royal Astronomical Society, 13(1967), 529–539.
  • [9]         M. Caputo and M. A. Fabrizio, New definition of fractional derivative without singular kernel, Progr Fract Differ Appl, 1(2015), 73–85.
  • [10]       V. F. M. Delgado, J. F. G´omez-Aguilar, H. Y´epez-Mart ´ınez, D. Baleanu, R. F. Escobar-Jimenez, and V. H. Olivares-Peregrino, Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular, Advances in Difference Equations, 164 (2016), 1-17.
  • [11]       M. H. Derakhshan, M. A. Darani, A. Ansari, and R. K. Ghaziani, On asymptotic stability of Prabhakar fractional differential systems, Computational methods for differential equations, 4(4) (2016), 276-284.
  • [12]       M. A. El-Tawil and S. N. Huseen, On Convergence of q-Homotopy Analysis Method, Int. J. Contemp. Math. Sciences, 8 (2013), 481-497.
  • [13]       A. Erdelyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi, Higher Transcedential Functions, Vol. 3. McGraw- Hill, New York, 1955.
  • [14]       R. Garra and R. Garrappa, The Prabhakar or three parameter Mittag–Leffler function: theory and application, Communications in Nonlinear Science and Numerical Simulation, 56 (2018), 314-329.
  • [15]       R. Garra, R. Goreno, F. Polito, and Z. Tomovski, Hilfer-Prabhakar Derivative and Some Applications, Applied Mathematics and Computation, 242(2014), 576-589.
  • [16]       V. Gu¨lkac, The homotopy perturbation method for the BlackScholes equation, J Stat Comput Simul, 80 (2010), 1349-1354.
  • [17]       O. Guner and A. Bekir, Solving nonlinear space-time fractional differential equations via ansatz method, Compu- tational methods for differential equations, 6(1) (2018), 1-11.
  • [18]       A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam: Elsevier, 2006.
  • [19]       S. Kumar, D. Kumar, and J. Singh, Numerical computation of fractional BlackeScholes equation arising in finan- cial market, egyptian journal of basic and applied sciences, 1 (2014), 177 -183.
  • [20]       F. Mainardi, Fractional Calculus and Waves in Linear Visco-elasticity: An Introduction to Mathematical Models, Imperial College Press, London, 2010.
  • [21]       K. S. Miller and B. Ross, An Introduction to the Fractional Integrals and Derivatives, Theory and Applications, New York, 1993.
  • [22]       S. Mockary, A. Vahidi, and E. Babolian, An efficient approximate solution of Riesz fractional advection-diffusion equation, Computational Methods for Differential Equations, , 10(2) (2022), 307-319. DOI: 10.22034/CMDE.2021.41690.1815.
  • [23]       K.B. Oldham and J. Spanier, The Fractional Calculus, New York, 1974.
  • [24]       S. K. Panchal, Pravinkumar V. Dole, and Amol D. Khandagale, k-Hilfer-Prabhakar Fractional Derivatives and its Applications, Indian J. Math, 59( 2017), 367-383.
  • [25]       R. K. Pandey and H. K. Mishra, Homotopy analysis Sumudu transform method for time—fractional third order dispersive partial differential equation, Adv. Comput. Math., 43(2017), 365–383.
  • [26]       T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J, 19 (1971), 7-15.
  • [27]       I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [28]       J. Rashidinia and E. Mohmedi, Numerical solution for solving fractional parabolic partial differential equations, Computational Methods for Differential Equations, 10(1) (2022), 121-143. DOI: 10.22034/CMDE.2021.41150.1787.
  • [29]       N. H. Sweilam, A. M. Nagy, and A. A. EL-Sayed, Sinc-Chebyshev Collocation Method for Time-Fractional Order Telegraph Equation, Applied and computational mathematics, 19(2) (2020), 162-174.
  • [30]       G. K. Watugala, Sumudu Transform- an Integral transform to solve differential equations and control engineering problems, Internat. J. Math. Ed. Sci. Tech, 24(1993), 35-43.
  • [31]       A. Wiman, U¨ber den fundamental satz in der teorie der funktionen Eα(x)., Acta Math., 29 (1905), 191–201.
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