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On the Study of Pantograph Differential Equations with Proportional Fractional Derivative

Yıl 2023, Cilt: 11 Sayı: 2, 97 - 103, 30.06.2023
https://doi.org/10.36753/mathenot.1057344

Öz

This manuscript is devoted to investigate the existence, uniqueness and stability of pantograph equations with Hilfer generalized proportional fractional derivative. The concerned results are obtained using standard theorems.

Destekleyen Kurum

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Proje Numarası

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Kaynakça

  • [1] R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear. Sci. Numer. Simulat., 44 (2017) 460–481.
  • [2] S. Abbas, M. Benchohra, S. Sivasundaram, Dynamics and Ulam stability for Hilfer type fractional di?erential equations, Nonlinear Stud., 4 (2016) 627–637.
  • [3] I. Ahmed, P. Kumam, F. Jarad, P. Borisut, W. Jirakitpuwapat, On Hilfer generalized proportional fractional derivative, Adv. Di?er. Equ. 2020:329.
  • [4] K. Balachandran, S. Kiruthika, J.J. Trujillo, Existence of solutions of Nonlinear fractional pantograph equations, Acta Math. Sci., 33B (2013) 1-9.
  • [5] K. M. Furati, M. D. Kassim, N. E. Tatar, Existence and uniqueness for a problem involving HFD, Compur. Math. Appl., 64 (2012) 1616–1626.
  • [6] K. Guan, Q. Wang, X. He, Oscillation of a pantograph di?erential equation with impulsive perturbations, Appl. Math. Comput. , 219 (2012) 3147-3153.
  • [7] R. Hilfer, Application of fractional Calculus in Physics, World Scientific, Singapore, 1999.
  • [8] A. Iserles, On the generalized pantograph functional di?erential equation, Eur. J. Appl. Math., 4 (1993) 1-38.
  • [9] A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Di?erential Equations, in: Mathematics Studies, vol.204, Elsevier, 2006.
  • [10] R. Kamocki, C. Obcznnski, On fractional Cauchy-type problems containing Hilfer derivative, Electron. J. Qual. Theory. Di?er. Equ., 50 (2016) 1–12.
  • [11] I. Podlubny, Fractional Di?erential Equations: Mathematics in Science and Engineering, vol. 198, Acad. Press, 1999.
  • [12] D. R. Smart, Fixed Point Theorems, Cambridge University Press, 1980.
  • [13] J.VanterlerdaC.Sousa, E.CapelasdeOliveira, Onthe?-Hilferfractionalderivative, Commun.Nonlinear. Sci. Numer. Simulat., 60 2018, 72-91.
  • [14] J. Vanterlerda C. Sousa, E. Capelas de Oliveira, On the Ulam-Hyers-Rassias satibility for nonlinear fractional di?erential equations using the ?-Hilfer operator, arXiv: 1711.07339, (2017).
  • [15] D. Vivek, K. Kanagarajan, S. Sivasundaram, Dynamics and stability of pantograph equationsvia Hilfer fractional derivative, Nonlinear Stud., 23 (2016) 685-698.
Yıl 2023, Cilt: 11 Sayı: 2, 97 - 103, 30.06.2023
https://doi.org/10.36753/mathenot.1057344

Öz

Proje Numarası

-

Kaynakça

  • [1] R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear. Sci. Numer. Simulat., 44 (2017) 460–481.
  • [2] S. Abbas, M. Benchohra, S. Sivasundaram, Dynamics and Ulam stability for Hilfer type fractional di?erential equations, Nonlinear Stud., 4 (2016) 627–637.
  • [3] I. Ahmed, P. Kumam, F. Jarad, P. Borisut, W. Jirakitpuwapat, On Hilfer generalized proportional fractional derivative, Adv. Di?er. Equ. 2020:329.
  • [4] K. Balachandran, S. Kiruthika, J.J. Trujillo, Existence of solutions of Nonlinear fractional pantograph equations, Acta Math. Sci., 33B (2013) 1-9.
  • [5] K. M. Furati, M. D. Kassim, N. E. Tatar, Existence and uniqueness for a problem involving HFD, Compur. Math. Appl., 64 (2012) 1616–1626.
  • [6] K. Guan, Q. Wang, X. He, Oscillation of a pantograph di?erential equation with impulsive perturbations, Appl. Math. Comput. , 219 (2012) 3147-3153.
  • [7] R. Hilfer, Application of fractional Calculus in Physics, World Scientific, Singapore, 1999.
  • [8] A. Iserles, On the generalized pantograph functional di?erential equation, Eur. J. Appl. Math., 4 (1993) 1-38.
  • [9] A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Di?erential Equations, in: Mathematics Studies, vol.204, Elsevier, 2006.
  • [10] R. Kamocki, C. Obcznnski, On fractional Cauchy-type problems containing Hilfer derivative, Electron. J. Qual. Theory. Di?er. Equ., 50 (2016) 1–12.
  • [11] I. Podlubny, Fractional Di?erential Equations: Mathematics in Science and Engineering, vol. 198, Acad. Press, 1999.
  • [12] D. R. Smart, Fixed Point Theorems, Cambridge University Press, 1980.
  • [13] J.VanterlerdaC.Sousa, E.CapelasdeOliveira, Onthe?-Hilferfractionalderivative, Commun.Nonlinear. Sci. Numer. Simulat., 60 2018, 72-91.
  • [14] J. Vanterlerda C. Sousa, E. Capelas de Oliveira, On the Ulam-Hyers-Rassias satibility for nonlinear fractional di?erential equations using the ?-Hilfer operator, arXiv: 1711.07339, (2017).
  • [15] D. Vivek, K. Kanagarajan, S. Sivasundaram, Dynamics and stability of pantograph equationsvia Hilfer fractional derivative, Nonlinear Stud., 23 (2016) 685-698.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Harikrishnan Sugumaran

Dvivek Vivek

Elsayed Elsayed 0000-0003-0894-8472

Proje Numarası -
Yayımlanma Tarihi 30 Haziran 2023
Gönderilme Tarihi 13 Ocak 2022
Kabul Tarihi 31 Aralık 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 11 Sayı: 2

Kaynak Göster

APA Sugumaran, H., Vivek, D., & Elsayed, E. (2023). On the Study of Pantograph Differential Equations with Proportional Fractional Derivative. Mathematical Sciences and Applications E-Notes, 11(2), 97-103. https://doi.org/10.36753/mathenot.1057344
AMA Sugumaran H, Vivek D, Elsayed E. On the Study of Pantograph Differential Equations with Proportional Fractional Derivative. Math. Sci. Appl. E-Notes. Haziran 2023;11(2):97-103. doi:10.36753/mathenot.1057344
Chicago Sugumaran, Harikrishnan, Dvivek Vivek, ve Elsayed Elsayed. “On the Study of Pantograph Differential Equations With Proportional Fractional Derivative”. Mathematical Sciences and Applications E-Notes 11, sy. 2 (Haziran 2023): 97-103. https://doi.org/10.36753/mathenot.1057344.
EndNote Sugumaran H, Vivek D, Elsayed E (01 Haziran 2023) On the Study of Pantograph Differential Equations with Proportional Fractional Derivative. Mathematical Sciences and Applications E-Notes 11 2 97–103.
IEEE H. Sugumaran, D. Vivek, ve E. Elsayed, “On the Study of Pantograph Differential Equations with Proportional Fractional Derivative”, Math. Sci. Appl. E-Notes, c. 11, sy. 2, ss. 97–103, 2023, doi: 10.36753/mathenot.1057344.
ISNAD Sugumaran, Harikrishnan vd. “On the Study of Pantograph Differential Equations With Proportional Fractional Derivative”. Mathematical Sciences and Applications E-Notes 11/2 (Haziran 2023), 97-103. https://doi.org/10.36753/mathenot.1057344.
JAMA Sugumaran H, Vivek D, Elsayed E. On the Study of Pantograph Differential Equations with Proportional Fractional Derivative. Math. Sci. Appl. E-Notes. 2023;11:97–103.
MLA Sugumaran, Harikrishnan vd. “On the Study of Pantograph Differential Equations With Proportional Fractional Derivative”. Mathematical Sciences and Applications E-Notes, c. 11, sy. 2, 2023, ss. 97-103, doi:10.36753/mathenot.1057344.
Vancouver Sugumaran H, Vivek D, Elsayed E. On the Study of Pantograph Differential Equations with Proportional Fractional Derivative. Math. Sci. Appl. E-Notes. 2023;11(2):97-103.

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