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On $\psi$-Hilfer fractional differential equation with complex order

Year 2018, Volume: 1 Issue: 1, 33 - 38, 11.03.2018

Harikrishnan Sugumaran , Rabha Ibrahim , Kuppusamy Kanagarajan

https://doi.org/10.32323/ujma.393130
Cited By: 11

Abstract

The objectives of this paper is to investigate some adequate results for the existence of solution to a $\psi$-Hilfer fractional derivatives (HFDEs) involving complex order. Appropriate conditions for the existence of at least one solution are developed by using Schauder fixed point theorem (SFPT) to the consider problem. Moreover, we also investigate the Ulam-Hyers stability for the proposed problem.

Keywords

Fractional derivative Existence Ulam-Hyers-Rassias stability Complex order

References

  • [1] R. Hilfer, Applications of fractional Calculus in Physics, World scientific, Singapore, 1999.
  • [2] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006.
  • [3] X.-Jun. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher Limited, Hong Kong, 2011.
  • [4] Jumarie, G. Maximum Entropy, Information Without Probability and Complex Fractals: Classical and Quantum Approach, 112, Springer Science & Business Media 2013.
  • [5] X-Jun Yang, D. Baleanu and H. M. Srivastava, Local Fractional Integral Transforms and Their Applications, Published by Elsevier Ltd (2016).
  • [6] R. W. Ibrahim, Fractional calculus of Multi-objective functions & Multi-agent systems. LAMBERT Academic Publishing, Saarbrcken, Germany 2017.
  • [7] J. Vanterler da C. Sousa, E. Capelas de Oliveira, On the $\psi$-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul.. In Press, Accepted Manuscript-2018.
  • [8] R.W. Ibrahim, Generalized Ulam-Hyers stability for fractional differential equations.” International Journal of Mathematics 23.05 (2012) 1250056.
  • [9] R.W. Ibrahim, Ulam stability for fractional differential equation in complex domain, Abstract and Applied Analysis. Vol. 2012. Hindawi, 2012.
  • [10] R.W. Ibrahim, Ulam-Hyers stability for Cauchy fractional differential equation in the unit disk, Abstract and Applied Analysis. Vol. 2012. Hindawi, 2012.
  • [11] R.W. Ibrahim and H. A. Jalab, Existence of Ulam stability for iterative fractional differential equations based on fractional entropy. Entropy 17.5 (2015) 3172-3181.
  • [12] D. Vivek, K. Kanagarajan and S. Sivasundaram, Theory and analysis of nonlinear neutral pantograph equations via Hilfer fractional derivative, Nonlinear Stud. 24(3) (2017),699-712.
  • [13] J. Wang and Y. Zhang, Nonlocal initial value problem for differential equations with Hilfer fractional derivative, Appl. Math. Comput. 266 2015, 850-859.

Year 2018, Volume: 1 Issue: 1, 33 - 38, 11.03.2018

Harikrishnan Sugumaran , Rabha Ibrahim , Kuppusamy Kanagarajan

https://doi.org/10.32323/ujma.393130
Cited By: 11

Abstract

References

  • [1] R. Hilfer, Applications of fractional Calculus in Physics, World scientific, Singapore, 1999.
  • [2] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, 2006.
  • [3] X.-Jun. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher Limited, Hong Kong, 2011.
  • [4] Jumarie, G. Maximum Entropy, Information Without Probability and Complex Fractals: Classical and Quantum Approach, 112, Springer Science & Business Media 2013.
  • [5] X-Jun Yang, D. Baleanu and H. M. Srivastava, Local Fractional Integral Transforms and Their Applications, Published by Elsevier Ltd (2016).
  • [6] R. W. Ibrahim, Fractional calculus of Multi-objective functions & Multi-agent systems. LAMBERT Academic Publishing, Saarbrcken, Germany 2017.
  • [7] J. Vanterler da C. Sousa, E. Capelas de Oliveira, On the $\psi$-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul.. In Press, Accepted Manuscript-2018.
  • [8] R.W. Ibrahim, Generalized Ulam-Hyers stability for fractional differential equations.” International Journal of Mathematics 23.05 (2012) 1250056.
  • [9] R.W. Ibrahim, Ulam stability for fractional differential equation in complex domain, Abstract and Applied Analysis. Vol. 2012. Hindawi, 2012.
  • [10] R.W. Ibrahim, Ulam-Hyers stability for Cauchy fractional differential equation in the unit disk, Abstract and Applied Analysis. Vol. 2012. Hindawi, 2012.
  • [11] R.W. Ibrahim and H. A. Jalab, Existence of Ulam stability for iterative fractional differential equations based on fractional entropy. Entropy 17.5 (2015) 3172-3181.
  • [12] D. Vivek, K. Kanagarajan and S. Sivasundaram, Theory and analysis of nonlinear neutral pantograph equations via Hilfer fractional derivative, Nonlinear Stud. 24(3) (2017),699-712.
  • [13] J. Wang and Y. Zhang, Nonlocal initial value problem for differential equations with Hilfer fractional derivative, Appl. Math. Comput. 266 2015, 850-859.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Harikrishnan Sugumaran

Rabha Ibrahim

Kuppusamy Kanagarajan This is me

Submission Date February 17, 2018
Acceptance Date March 6, 2018
Publication Date March 11, 2018
Published in Issue Year 2018 Volume: 1 Issue: 1

Cite

APA Sugumaran, H., Ibrahim, R., & Kanagarajan, K. (2018). On $\psi$-Hilfer fractional differential equation with complex order. Universal Journal of Mathematics and Applications, 1(1), 33-38. https://doi.org/10.32323/ujma.393130
AMA 1.Sugumaran H, Ibrahim R, Kanagarajan K. On $\psi$-Hilfer fractional differential equation with complex order. Univ. J. Math. Appl. 2018;1(1):33-38. doi:10.32323/ujma.393130
Chicago Sugumaran, Harikrishnan, Rabha Ibrahim, and Kuppusamy Kanagarajan. 2018. “On $\psi$-Hilfer Fractional Differential Equation With Complex Order”. Universal Journal of Mathematics and Applications 1 (1): 33-38. https://doi.org/10.32323/ujma.393130.
EndNote Sugumaran H, Ibrahim R, Kanagarajan K (March 1, 2018) On $\psi$-Hilfer fractional differential equation with complex order. Universal Journal of Mathematics and Applications 1 1 33–38.
IEEE [1]H. Sugumaran, R. Ibrahim, and K. Kanagarajan, “On $\psi$-Hilfer fractional differential equation with complex order”, Univ. J. Math. Appl., vol. 1, no. 1, pp. 33–38, Mar. 2018, doi: 10.32323/ujma.393130.
ISNAD Sugumaran, Harikrishnan - Ibrahim, Rabha - Kanagarajan, Kuppusamy. “On $\psi$-Hilfer Fractional Differential Equation With Complex Order”. Universal Journal of Mathematics and Applications 1/1 (March 1, 2018): 33-38. https://doi.org/10.32323/ujma.393130.
JAMA 1.Sugumaran H, Ibrahim R, Kanagarajan K. On $\psi$-Hilfer fractional differential equation with complex order. Univ. J. Math. Appl. 2018;1:33–38.
MLA Sugumaran, Harikrishnan, et al. “On $\psi$-Hilfer Fractional Differential Equation With Complex Order”. Universal Journal of Mathematics and Applications, vol. 1, no. 1, Mar. 2018, pp. 33-38, doi:10.32323/ujma.393130.
Vancouver 1.Sugumaran H, Ibrahim R, Kanagarajan K. On $\psi$-Hilfer fractional differential equation with complex order. Univ. J. Math. Appl. [Internet]. 2018 Mar. 1;1(1):33-8. Available from: https://izlik.org/JA34US27FR

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