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

Harikrishnan Sugumaran; Rabha Ibrahim; Kuppusamy Kanagarajan

doi:10.32323/ujma.393130

EN

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

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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Harikrishnan Sugumaran ^*
Oman

Rabha Ibrahim
Oman

Kuppusamy Kanagarajan This is me
Oman

Publication Date

March 11, 2018

Submission Date

February 17, 2018

Acceptance Date

March 6, 2018

Published in Issue

Year 2018 Volume: 1 Number: 1

DOI

https://doi.org/10.32323/ujma.393130

IZ

https://izlik.org/JA34US27FR

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.Harikrishnan Sugumaran, Rabha Ibrahim, Kuppusamy Kanagarajan. On $\psi$-Hilfer fractional differential equation with complex order. Univ. J. Math. Appl. 2018 Mar. 1;1(1):33-8. doi:10.32323/ujma.393130