Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, , 297 - 310, 31.08.2023
https://doi.org/10.18185/erzifbed.1220243

Öz

Kaynakça

  • [1] Petras, I. (2011). Fractional-order nonlinear systems modeling, Analysis and Simulation, Springer. New York.
  • [2] Ashyralyev A. (2009). A note on fractional derivatives and fractional powers of operators. JMAA. 357; 232-236.
  • [3] Ashyralyev A. (2013). Well-posedness of fractional parabolic equations, Boundary Value Problems. 31; 1-18.
  • [4] Ashyralyev A. and Cakir, Z. (2013). FDM for fractional parabolic equations with the Neumann condition. Advances in Difference Equations, 2013(120), doi:10.1186/1687-1847-2013-120.
  • [5] Ashyralyev A., Emirov N. and Cakir Z. (2014). Well-posedness of fractional parabolic differential and difference equations with Dirchlet-Neumann condition, Electronic Journal of Differential Equations. 2014 (97); 1-17.
  • [6] Podlubny, I. (1999). Fractional differential equations. Mathematics in science and engineering, vol 198. Academic Press. San Diego.
  • [7] Samko S.G., Kilbas A.A., Marichev O.I. (1993). Fractional Integrals and Derivatives. Gordon & Breach. Yverdon.
  • [8] Baleanu D, Garra, R, Petras, I. (2013). A fractional variational approach to the fractional Basset-Type equation, Reports on Mathematical Physics. 72 (1); 57-64.
  • [9] Diethelm, K. and Ford, J.N. (2002). Analysis of fractional differential equations. JMAA. 265; 229-248.
  • [10] Cona, L. (2017). Fixed point approach to Basset problem. New Trends in Mathematical Sciences. 5(3); 175-181.
  • [11] Cona, L. (2017). Fixed point approach to Bagley Torvik problem. Communication in Mathematical Modeling and Applications. 2(3), 50--57.
  • [12] Bai, Z., Sun, S. and Chen, Y.Q. (2014).The existence and uniqueness of a class of fractional differential equations. Abstract and Applied Analysis, Hindawi Publishing Corporation.2014;1-6.
  • [13] Ashyralyev A. (2013). Computational mathematics textbook, Shymkent.
  • [14] Kimeu, Joseph M. (2009). Fractional calculus: Definitions and applications. Masters Theses & Specialist Projects. Paper 115. (https://digitalcommons.wku.edu/theses/115)
  • [15] Kreyszig, E. (1978). Introductory functional analysis with applications, John Willey & Sons, New York.
  • [16] Caputo, M., Fabrizo, M. (2015). A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl., 1(2), 73-85.
  • [17] Atangana, A. Baleanu, D. (2016). New fractional derivative with non-local and non-singular kernel, Therm. Sci., 20(2), 757-763.
  • [18] Yang, X.J., Sirivasta, H.M., Machado, J.A.T. (2016). A new fractional derivatives without singular kernel: application to the modelling of the steady heat flow, Therm. Sci., 20, 753-756.
  • [19] Vanterler da Sausa, J., Capelas de Oliveira C., E. (2017). A new fractional derivative of variable order with non-singular order and fractional differential equations, arXiv: 1712.06506v1.
  • [20] Vanterler da Sausa, J., Capelas de Oliveira C., E. (2020). On the Ψ-Hilfer fractional derivative, Commun Nonlinear Sci. Numer, Simul. 60, 72-91.

On Existence and Uniqueness of Some Fractional Order Integro-Differential Equation

Yıl 2023, , 297 - 310, 31.08.2023
https://doi.org/10.18185/erzifbed.1220243

Öz

In this study, a sufficient condition for the existence and uniqueness of some fractional order Integral-Differential equations is obtained. Therefore, the fixed point method is used to solve the differential equation problem involving nonlinear degree integrals. In addition, the results found is supported by examples.

Kaynakça

  • [1] Petras, I. (2011). Fractional-order nonlinear systems modeling, Analysis and Simulation, Springer. New York.
  • [2] Ashyralyev A. (2009). A note on fractional derivatives and fractional powers of operators. JMAA. 357; 232-236.
  • [3] Ashyralyev A. (2013). Well-posedness of fractional parabolic equations, Boundary Value Problems. 31; 1-18.
  • [4] Ashyralyev A. and Cakir, Z. (2013). FDM for fractional parabolic equations with the Neumann condition. Advances in Difference Equations, 2013(120), doi:10.1186/1687-1847-2013-120.
  • [5] Ashyralyev A., Emirov N. and Cakir Z. (2014). Well-posedness of fractional parabolic differential and difference equations with Dirchlet-Neumann condition, Electronic Journal of Differential Equations. 2014 (97); 1-17.
  • [6] Podlubny, I. (1999). Fractional differential equations. Mathematics in science and engineering, vol 198. Academic Press. San Diego.
  • [7] Samko S.G., Kilbas A.A., Marichev O.I. (1993). Fractional Integrals and Derivatives. Gordon & Breach. Yverdon.
  • [8] Baleanu D, Garra, R, Petras, I. (2013). A fractional variational approach to the fractional Basset-Type equation, Reports on Mathematical Physics. 72 (1); 57-64.
  • [9] Diethelm, K. and Ford, J.N. (2002). Analysis of fractional differential equations. JMAA. 265; 229-248.
  • [10] Cona, L. (2017). Fixed point approach to Basset problem. New Trends in Mathematical Sciences. 5(3); 175-181.
  • [11] Cona, L. (2017). Fixed point approach to Bagley Torvik problem. Communication in Mathematical Modeling and Applications. 2(3), 50--57.
  • [12] Bai, Z., Sun, S. and Chen, Y.Q. (2014).The existence and uniqueness of a class of fractional differential equations. Abstract and Applied Analysis, Hindawi Publishing Corporation.2014;1-6.
  • [13] Ashyralyev A. (2013). Computational mathematics textbook, Shymkent.
  • [14] Kimeu, Joseph M. (2009). Fractional calculus: Definitions and applications. Masters Theses & Specialist Projects. Paper 115. (https://digitalcommons.wku.edu/theses/115)
  • [15] Kreyszig, E. (1978). Introductory functional analysis with applications, John Willey & Sons, New York.
  • [16] Caputo, M., Fabrizo, M. (2015). A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl., 1(2), 73-85.
  • [17] Atangana, A. Baleanu, D. (2016). New fractional derivative with non-local and non-singular kernel, Therm. Sci., 20(2), 757-763.
  • [18] Yang, X.J., Sirivasta, H.M., Machado, J.A.T. (2016). A new fractional derivatives without singular kernel: application to the modelling of the steady heat flow, Therm. Sci., 20, 753-756.
  • [19] Vanterler da Sausa, J., Capelas de Oliveira C., E. (2017). A new fractional derivative of variable order with non-singular order and fractional differential equations, arXiv: 1712.06506v1.
  • [20] Vanterler da Sausa, J., Capelas de Oliveira C., E. (2020). On the Ψ-Hilfer fractional derivative, Commun Nonlinear Sci. Numer, Simul. 60, 72-91.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Lale Cona 0000-0002-2744-1960

Esmahan Bal 0000-0002-0135-9176

Erken Görünüm Tarihi 24 Ağustos 2023
Yayımlanma Tarihi 31 Ağustos 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Cona, L., & Bal, E. (2023). On Existence and Uniqueness of Some Fractional Order Integro-Differential Equation. Erzincan University Journal of Science and Technology, 16(2), 297-310. https://doi.org/10.18185/erzifbed.1220243