Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 9 Sayı: 1, 143 - 147, 28.04.2021

Öz

Kaynakça

  • [1] S. Abbas, M. Benchohra, J. Lazreg and Y. Zhou, A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability, Chaos, Solitons & Fractals, Vol:102, (2017), 47-71.
  • [2] S. Abbas, M. Benchohra, J. Lazreg and Y. Zhou, Existence and Ulam stability for fractional differential equations of Hilfer-Hadamard type, Advances in Difference Equations, Vol:180, (2017), 1-14.
  • [3] B. Ahmad, S. Ntouyas and J. Tariboon, A study of mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions via endpoint theory, Applied Mathematics Letters, Vol:52, (2016), 9-14.
  • [4] P. Butzer, A. Kilbas and J. Trujillo, Compositions of Hadamard-type fractional integration operators and the semigroup property, J. Math. Anal. Appl. Vol:269, (2002), 387-400.
  • [5] B. Ahmad and S. Ntouyas, Initial-value problems for hybrid Hadamard fractional differential equations, Electronic Journal of Differential Equations, Vol:2014, No. 161 (2014), 1-8.
  • [6] L. Dawood, A. Hamoud and N. Mohammed, Laplace discrete decomposition method for solving nonlinear Volterra-Fredholm integro-differential equations, Journal of Mathematics and Computer Science, Vol:21, No.2 (2020), 158-163.
  • [7] J. Hadamard, Essai sur letude` des fonctions donnees` par leur developpement` de Taylor, J. Mat. Pure Appl. Ser. Vol:4, No.8 (1892), 101-186.
  • [8] A. Hamoud, Existence and uniqueness of solutions for fractional neutral Volterra-Fredholm integro-differential equations, Advances in the Theory of Nonlinear Analysis and its Application, Vol:4, No.4 (2020), 321-331.
  • [9] A. Hamoud, N. Mohammed and K. Ghadle, Existence and uniqueness results for Volterra-Fredholm integro-differential equations, Advances in the Theory of Nonlinear Analysis and its Application, Vol:4, No.4 (2020), 361-372.
  • [10] A. Hamoud and K. Ghadle, The approximate solutions of fractional Volterra-Fredholm integro-differential equations by using analytical techniques, Probl. Anal. Issues Anal., Vol:7 (25), No.1 (2018), 41-58.
  • [11] A. Hamoud and K. Ghadle, Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations, J. Math. Model., Vol:6, No. 1 (2018), 91-104.
  • [12] A. Hamoud and K. Ghadle, Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind, Tamkang J. Math. Vol:49, No.4 (2018), 301-315.
  • [13] A. Hamoud and K. Ghadle, Existence and uniqueness of solutions for fractional mixed Volterra-Fredholm integro-differential equations, Indian J. Math. Vol:60, No.3 (2018), 375-395.
  • [14] A. Hamoud, K. Ghadle and S. Atshan, The approximate solutions of fractional integro-differential equations by using modified Adomian decomposition method, Khayyam J. Math. Vol:5, No.1 (2019), 21-39.
  • [15] A. Hamoud and K. Ghadle, Some new existence, uniqueness and convergence results for fractional Volterra-Fredholm integro-differential equations, J. Appl. Comput. Mech. Vol:5, No.1 (2019), 58-69.
  • [16] K. Karthikeyan and J. Trujillo, Existence and uniqueness results for fractional integro-differential equations with boundary value conditions, Commun. Nonlinear Sci. Numer. Simulat., Vol:17, (2012), 4037-4043.
  • [17] A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc. Vol:38, (2001), 1191-1204.
  • [18] A. Kilbas, H. Srivastava and J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud., Elsevier, Amsterdam, Vol:204, 2006.
  • [19] V. Lakshmikantham and M. Rao, Theory of Integro-Differential Equations, Gordon & Breach, London, 1995.
  • [20] K. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
  • [21] S. Samko, A. Kilbas and O. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.
  • [22] J. Wang, Y. Zhou and M. Medved, Existence and stability of fractional differential equations with Hadamard derivative, Topological Methods in Nonlinear Analysis, Vol:41, No.1 (2013), 113-133.
  • [23] J. Wu and Y. Liu, Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spaces, Electronic Journal of Differential Equations, Vol:2009, (2009), 1-8.
  • [24] J. Wu and Y. Liu, Existence and uniqueness results for fractional integro-differential equations with nonlocal conditions, 2nd IEEE International Conference on Information and Financial Engineering, (2010), 91-94.
  • [25] Y. Zhou, Basic Theory of Fractional Differential Equations, Singapore: World Scientific, 2014.

Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations

Yıl 2021, Cilt: 9 Sayı: 1, 143 - 147, 28.04.2021

Öz

In this paper, we establish some new conditions for the existence and uniqueness of solutions for a class of nonlinear Hadamard fractional Volterra-Fredholm integro-differential equations with initial conditions. The desired results are proved by using Arzela-Ascoli theorem aid of fixed point theorems due to Banach and Krasnoselskii in Banach spaces. 

Kaynakça

  • [1] S. Abbas, M. Benchohra, J. Lazreg and Y. Zhou, A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability, Chaos, Solitons & Fractals, Vol:102, (2017), 47-71.
  • [2] S. Abbas, M. Benchohra, J. Lazreg and Y. Zhou, Existence and Ulam stability for fractional differential equations of Hilfer-Hadamard type, Advances in Difference Equations, Vol:180, (2017), 1-14.
  • [3] B. Ahmad, S. Ntouyas and J. Tariboon, A study of mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions via endpoint theory, Applied Mathematics Letters, Vol:52, (2016), 9-14.
  • [4] P. Butzer, A. Kilbas and J. Trujillo, Compositions of Hadamard-type fractional integration operators and the semigroup property, J. Math. Anal. Appl. Vol:269, (2002), 387-400.
  • [5] B. Ahmad and S. Ntouyas, Initial-value problems for hybrid Hadamard fractional differential equations, Electronic Journal of Differential Equations, Vol:2014, No. 161 (2014), 1-8.
  • [6] L. Dawood, A. Hamoud and N. Mohammed, Laplace discrete decomposition method for solving nonlinear Volterra-Fredholm integro-differential equations, Journal of Mathematics and Computer Science, Vol:21, No.2 (2020), 158-163.
  • [7] J. Hadamard, Essai sur letude` des fonctions donnees` par leur developpement` de Taylor, J. Mat. Pure Appl. Ser. Vol:4, No.8 (1892), 101-186.
  • [8] A. Hamoud, Existence and uniqueness of solutions for fractional neutral Volterra-Fredholm integro-differential equations, Advances in the Theory of Nonlinear Analysis and its Application, Vol:4, No.4 (2020), 321-331.
  • [9] A. Hamoud, N. Mohammed and K. Ghadle, Existence and uniqueness results for Volterra-Fredholm integro-differential equations, Advances in the Theory of Nonlinear Analysis and its Application, Vol:4, No.4 (2020), 361-372.
  • [10] A. Hamoud and K. Ghadle, The approximate solutions of fractional Volterra-Fredholm integro-differential equations by using analytical techniques, Probl. Anal. Issues Anal., Vol:7 (25), No.1 (2018), 41-58.
  • [11] A. Hamoud and K. Ghadle, Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations, J. Math. Model., Vol:6, No. 1 (2018), 91-104.
  • [12] A. Hamoud and K. Ghadle, Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind, Tamkang J. Math. Vol:49, No.4 (2018), 301-315.
  • [13] A. Hamoud and K. Ghadle, Existence and uniqueness of solutions for fractional mixed Volterra-Fredholm integro-differential equations, Indian J. Math. Vol:60, No.3 (2018), 375-395.
  • [14] A. Hamoud, K. Ghadle and S. Atshan, The approximate solutions of fractional integro-differential equations by using modified Adomian decomposition method, Khayyam J. Math. Vol:5, No.1 (2019), 21-39.
  • [15] A. Hamoud and K. Ghadle, Some new existence, uniqueness and convergence results for fractional Volterra-Fredholm integro-differential equations, J. Appl. Comput. Mech. Vol:5, No.1 (2019), 58-69.
  • [16] K. Karthikeyan and J. Trujillo, Existence and uniqueness results for fractional integro-differential equations with boundary value conditions, Commun. Nonlinear Sci. Numer. Simulat., Vol:17, (2012), 4037-4043.
  • [17] A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc. Vol:38, (2001), 1191-1204.
  • [18] A. Kilbas, H. Srivastava and J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud., Elsevier, Amsterdam, Vol:204, 2006.
  • [19] V. Lakshmikantham and M. Rao, Theory of Integro-Differential Equations, Gordon & Breach, London, 1995.
  • [20] K. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.
  • [21] S. Samko, A. Kilbas and O. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Yverdon, 1993.
  • [22] J. Wang, Y. Zhou and M. Medved, Existence and stability of fractional differential equations with Hadamard derivative, Topological Methods in Nonlinear Analysis, Vol:41, No.1 (2013), 113-133.
  • [23] J. Wu and Y. Liu, Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spaces, Electronic Journal of Differential Equations, Vol:2009, (2009), 1-8.
  • [24] J. Wu and Y. Liu, Existence and uniqueness results for fractional integro-differential equations with nonlocal conditions, 2nd IEEE International Conference on Information and Financial Engineering, (2010), 91-94.
  • [25] Y. Zhou, Basic Theory of Fractional Differential Equations, Singapore: World Scientific, 2014.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Ahmed Hamoud 0000-0002-8877-7337

Abdulrahman Sharif Bu kişi benim

Aishwary K. Ghadle Bu kişi benim

Kirtiwant Ghadle

Yayımlanma Tarihi 28 Nisan 2021
Gönderilme Tarihi 10 Ağustos 2020
Kabul Tarihi 22 Eylül 2020
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 1

Kaynak Göster

APA Hamoud, A., Sharif, A., Ghadle, A. K., Ghadle, K. (2021). Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations. Konuralp Journal of Mathematics, 9(1), 143-147.
AMA Hamoud A, Sharif A, Ghadle AK, Ghadle K. Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations. Konuralp J. Math. Nisan 2021;9(1):143-147.
Chicago Hamoud, Ahmed, Abdulrahman Sharif, Aishwary K. Ghadle, ve Kirtiwant Ghadle. “Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations”. Konuralp Journal of Mathematics 9, sy. 1 (Nisan 2021): 143-47.
EndNote Hamoud A, Sharif A, Ghadle AK, Ghadle K (01 Nisan 2021) Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations. Konuralp Journal of Mathematics 9 1 143–147.
IEEE A. Hamoud, A. Sharif, A. K. Ghadle, ve K. Ghadle, “Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations”, Konuralp J. Math., c. 9, sy. 1, ss. 143–147, 2021.
ISNAD Hamoud, Ahmed vd. “Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations”. Konuralp Journal of Mathematics 9/1 (Nisan 2021), 143-147.
JAMA Hamoud A, Sharif A, Ghadle AK, Ghadle K. Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations. Konuralp J. Math. 2021;9:143–147.
MLA Hamoud, Ahmed vd. “Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations”. Konuralp Journal of Mathematics, c. 9, sy. 1, 2021, ss. 143-7.
Vancouver Hamoud A, Sharif A, Ghadle AK, Ghadle K. Existence and Uniqueness Results of Hadamard Fractional Volterra-Fredholm Integro-Differential Equations. Konuralp J. Math. 2021;9(1):143-7.
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