An Arbitrary Order Differential Equations on Times Scale

S. Harikrishnana; Rabha İbrahim; K. Kanagarajan

doi:10.32323/ujma.456191

EN

An Arbitrary Order Differential Equations on Times Scale

Abstract

Here existence and stability results of $\psi$-Hilfer fractional differential equations on time scales is obtained. Here sufficient condition for existence and uniqueness of solution by using Schauder's fixed point theorem (FPT) and Banach FPT is produced. In addition, generalized Ulam stability of the proposed problem is also discussed. problem.

Keywords

Fractional calculus,Existence,Ulam-Hyers-Rassias stability

References

[1] A. Ahmadkhanlu, M. Jahanshahi, On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales, Bull. Iranian Math. Soc., 38 (2012), 241-252.
[2] R. P. Agarwal, M. Bohner, Basic calculus on time scales and some of its applications, Results Math., 35 (1999), 3-22.
[3] N. Benkhettou, A. Hammoudi, D. F. M. Torres, Existence and uniqueness of solution for a fractional Riemann-lioville initial value problem on time scales, J. King Saud Univ. Sci., 28 (2016), 87-92.
[4] M. Bohner, A. Peterson, Advances in dynamic equations on time scales, Birkhauser, Boston, 2003.
[5] M. Bohner, A. Peterson, Dtnamica equations on times scale, Birkhauser, Boston, Boston, MA.
[6] K. M. Furati, M. D. Kassim, N.e-. Tatar, Existence and uniqueness for a problem involving Hilfer fractional derivative, Comput. Math. Appl., 64 (2012), 1616-1626.
[7] H. Gu, J. J. Trujillo, Existence of mild solution for evolution equation with Hilfer fractional derivative, Appl. Math. Comput., 15 (2015), 344-354.
[8] S. Harikrishnan, K. Shah, D. Baleanu, K. Kanagarajan, Note on the solution of random differential equations via y-Hilfer fractional derivative, Adv. Difference Equ., 2018(224) (2018).
[9] R. Hilfer, Application of fractional calculus in physics, World Scientific, Singapore, 1999.
[10] R. W. Ibrahim, Generalized Ulam-Hyers stability for fractional differential equations, Int. J. Math., 23 (2012).

[11] P. Muniyappan, S. Rajan, Hyers-Ulam-Rassias stability of fractional differential equation, Int. J. Pure Appl. Math., 102 (2015), 631-642.
[12] I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
[13] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, theory and applications, Gordon and Breach Sci. Publishers, Yverdon, 1993.
[14] J. Vanterler da C. Sousa, E. Capelas de Oliveira, On the y-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul., (in press).
[15] J. Vanterler da C. Sousa, E. Capelas de Oliveira, Ulam-Hyers stability of a nonlinear fractional Volterra integro-differential equation, Appl. Math. Lett., (in press).
[16] D. Vivek, K. Kanagarajan, E. M. Elsayed, Some existence and stability results for Hilfer-fractional implicit differential equations with nonlocal conditions, Mediterr. J. Math., 15 (2018), 1-15.
[17] J. Wang, L. Lv, Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Electron J. Qual. Theory Differ. Equ., 63 (2011), 1-10.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

S. Harikrishnana

Rabha İbrahim
Malaysia

K. Kanagarajan

Publication Date

December 20, 2018

Submission Date

August 31, 2018

Acceptance Date

September 26, 2018

Published in Issue

Year 2018 Volume: 1 Number: 4

DOI

https://doi.org/10.32323/ujma.456191

IZ

https://izlik.org/JA43SS54AU

APA

Harikrishnana, S., İbrahim, R., & Kanagarajan, K. (2018). An Arbitrary Order Differential Equations on Times Scale. Universal Journal of Mathematics and Applications, 1(4), 262-266. https://doi.org/10.32323/ujma.456191

AMA

1.Harikrishnana S, İbrahim R, Kanagarajan K. An Arbitrary Order Differential Equations on Times Scale. Univ. J. Math. Appl. 2018;1(4):262-266. doi:10.32323/ujma.456191

Chicago

Harikrishnana, S., Rabha İbrahim, and K. Kanagarajan. 2018. “An Arbitrary Order Differential Equations on Times Scale”. Universal Journal of Mathematics and Applications 1 (4): 262-66. https://doi.org/10.32323/ujma.456191.

EndNote

Harikrishnana S, İbrahim R, Kanagarajan K (December 1, 2018) An Arbitrary Order Differential Equations on Times Scale. Universal Journal of Mathematics and Applications 1 4 262–266.

IEEE

[1]S. Harikrishnana, R. İbrahim, and K. Kanagarajan, “An Arbitrary Order Differential Equations on Times Scale”, Univ. J. Math. Appl., vol. 1, no. 4, pp. 262–266, Dec. 2018, doi: 10.32323/ujma.456191.

ISNAD

Harikrishnana, S. - İbrahim, Rabha - Kanagarajan, K. “An Arbitrary Order Differential Equations on Times Scale”. Universal Journal of Mathematics and Applications 1/4 (December 1, 2018): 262-266. https://doi.org/10.32323/ujma.456191.

JAMA

1.Harikrishnana S, İbrahim R, Kanagarajan K. An Arbitrary Order Differential Equations on Times Scale. Univ. J. Math. Appl. 2018;1:262–266.

MLA

Harikrishnana, S., et al. “An Arbitrary Order Differential Equations on Times Scale”. Universal Journal of Mathematics and Applications, vol. 1, no. 4, Dec. 2018, pp. 262-6, doi:10.32323/ujma.456191.

Vancouver

1.S. Harikrishnana, Rabha İbrahim, K. Kanagarajan. An Arbitrary Order Differential Equations on Times Scale. Univ. J. Math. Appl. 2018 Dec. 1;1(4):262-6. doi:10.32323/ujma.456191