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فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

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Sadek, Lakhlifa. (1405). Novel $(\psi,\phi)$-fractional operators with exponential kernels: properties and applications to linear differential equations. سامانه مدیریت نشریات علمی, 14(3), 1408-1425. doi: 10.22034/cmde.2025.62416.2748
Lakhlifa Sadek. "Novel $(\psi,\phi)$-fractional operators with exponential kernels: properties and applications to linear differential equations". سامانه مدیریت نشریات علمی, 14, 3, 1405, 1408-1425. doi: 10.22034/cmde.2025.62416.2748
Sadek, Lakhlifa. (1405). 'Novel $(\psi,\phi)$-fractional operators with exponential kernels: properties and applications to linear differential equations', سامانه مدیریت نشریات علمی, 14(3), pp. 1408-1425. doi: 10.22034/cmde.2025.62416.2748
Sadek, Lakhlifa. Novel $(\psi,\phi)$-fractional operators with exponential kernels: properties and applications to linear differential equations. سامانه مدیریت نشریات علمی, 1405; 14(3): 1408-1425. doi: 10.22034/cmde.2025.62416.2748

Novel $(\psi,\phi)$-fractional operators with exponential kernels: properties and applications to linear differential equations

Computational Methods for Differential Equations
مقاله 25، دوره 14، شماره 3، مهر 2026، صفحه 1408-1425    اصل مقاله (497 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.62416.2748
نویسنده
Lakhlifa Sadek*
1. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamil Nadu, India. 2. Department of Mathematics, Faculty of Sciences and Technology, BP 34. Ajdir 32003 Al-Hoceima, Abdelmalek Essaadi University, Tetouan, Morocco.
چکیده
This study introduces novel generalized fractional derivatives known as $(\psi,\phi)$-fractional derivatives of the Riemann-Liouville and Caputo types, each incorporating exponential function kernels. These new operators offer distinct advantages, including a semi-group property and a seamless extension of the Riemann-Liouville (RL-FD) and Caputo fractional derivatives (C-FD), as well as integrals (RL-FI).  We explore the Laplace transform of these $(\psi,\phi)$-fractional derivatives and integrals, leveraging them to address linear $(\psi,\phi)$-fractional differential equations. Moreover, these fractional operators are general to classical fractional operators, cotangent fractional operators, and generalized proportional operators.
کلیدواژه‌ها
Linear $(\psi؛ \phi)$-fractional differential equations؛ $(\psi؛ \phi)$-fractional operators؛ Laplace transform
مراجع
  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279 (2015), 57–66.
  • [2] T. Abdeljawad and D. Baleanu, Monotonicity results for fractional difference operators with discrete exponential kernels, Advances in Difference Equations, 2017(1) (2017), 1–9.
  • [3] T. Abdeljawad and D. Baleanu, On fractional derivatives with exponential kernel and their discrete versions, Reports on Mathematical Physics, 80(1) (2017), 11–27.
  • [4] Y. Adjabi, F. Jarad, D. Baleanu, and T. Abdeljawad, On Cauchy problems with Caputo Hadamard fractional derivatives, Journal of Computational Analysis and Applications, 21(1) (2016), 661–681.
  • [5] D. R. Anderson and D. J. Ulness, Newly defined conformable derivatives, Advances in Dynamical Systems and Applications, 10(2) (2015), 109–137.
  • [6] D. R. Anderson, Second-order self-adjoint differential equations using a proportional-derivative controller, Communications in Applied Nonlinear Analysis, 24 (2017), 17–48.
  • [7] A. Atangana and D. Baleanu, New fractional derivative with non-local and non-singular kernel, Thermal Science, 20 (2016), 757.
  • [8] M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, Progress in Fractional Differentiation & Applications, 1(2) (2015), 73–85.
  • [9] L. Debnath, Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences, 2003(54) (2003), 3413–3442.
  • [10] Y. Y. Gambo, F. Jarad, D. Baleanu, and T. Abdeljawad, On Caputo modification of the Hadamard fractional derivatives, Advances in Difference Equations, 2014(1) (2014), 1–12.
  • [11] R. Hilfer, Applications of fractional calculus in physics, World Scientific (Ed.), 2000.
  • [12] F. Jarad, T. Abdeljawad, and D. Baleanu, Caputo-type modification of the Hadamard fractional derivatives, Advances in Difference Equations, 2012 (2012), 1–8.
  • [13] F. Jarad, T. Abdeljawad, and D. Baleanu, On the generalized fractional derivatives and their Caputo modification, Journal of Nonlinear Sciences and Applications, 10(5) (2017), 2607–2619.
  • [14] F. Jarad, T. Abdeljawad, and J. Alzabut, Generalized fractional derivatives generated by a class of local proportional derivatives, The European Physical Journal Special Topics, 226 (2017), 3457–3471.
  • [15] F. Jarad, E. Ugurlu, T. Abdeljawad, and D. Baleanu, On a new class of fractional operators, Advances in Difference Equations, 2017(1) (2017), 1–16.
  • [16] F. Jarad and T. Abdeljawad, Generalized fractional derivatives and Laplace transform, Discrete and Continuous Dynamical Systems - Series S, 13(3) (2020), 709–722.
  • [17] F. Jarad, M. A. Alqudah, and T. Abdeljawad, On more general forms of proportional fractional operators, Open Mathematics, 18(1) (2020), 167–176.
  • [18] U. N. Katugampola, New approach to a generalized fractional integral, Applied Mathematics and Computation, 218(3) (2011), 860–865.
  • [19] U. N. Katugampola, A new approach to generalized fractional derivatives, Bulletin of Mathematical Analysis and Applications, 6 (2014), 1–15.
  • [20] R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264 (2014), 65–70.
  • [21] A. A. Kilbas, M. Saigo, and R. K. Saxena, Generalized Mittag-Leffler function and generalized fractional calculus operators, Integral Transforms and Special Functions, 15(1) (2004), 31–49.
  • [22] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, 204 (2006).
  • [23] A. N. Kochubei, General fractional calculus, evolution equations, and renewal processes, Integral Equations and Operator Theory, 71(4) (2011), 583–600.
  • [24] J. Losada and J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progress in Fractional Differentiation & Applications, 1(2) (2015), 87–92.
  • [25] R. L. Magin, Fractional calculus in bioengineering, Begell House Publishers, 2006.
  • [26] I. Podlubny, Fractional differential equations, Academic Press, San Diego, California, USA, 1999.
  • [27] L. Sadek, A Cotangent Fractional Derivative with the Application, Fractal and Fractional, 7(6) (2023), 444.
  • [28] L. Sadek and T. A. Lazar, On Hilfer cotangent fractional derivative and a particular class of fractional problems, AIMS Mathematics, 8(12) (2023), 28334–28352.
  • [29] L. Sadek, Controllability, observability, and stability of ϕ-conformable fractional linear dynamical systems, Asian Journal of Control, 26(5) (2024), 2476-2494.
  • [30] L. Sadek, D. Baleanu, M. S. Abdo, and W. Shatanawi, Introducing novel θ-fractional operators: Advances in fractional calculus, Journal of King Saud University–Science, 36(9) (2024), 103352.
  • [31] L. Sadek and F. Jarad, The general Caputo–Katugampola fractional derivative and numerical approach for solving the fractional differential equations, Alexandria Engineering Journal, 121 (2025), 539-557.
  • [32] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional integrals and derivatives: theory and applications, Gordon and Breach, Yverdon, 1993.
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