Research Article

Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations with Boundary Conditions

Volume: 7 Number: 2 October 15, 2019
EN

Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations with Boundary Conditions

Abstract

In this paper, we consider the existence and Ulam stability of solutions to the boundary value problem for implicit differential equations involving Hilfer fractional derivative. With the help of properties of Hilfer fractional calculus and fixed point methods, we derive existence and stability results.

Keywords

References

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  4. [4] B. Ahmad, J. J. Nieto, Riemann-Liouville fractional differential equations with fractional boundary conditions, Fixed point Theory, 13(2) (2012), 329-336.
  5. [5] Sz.Andras, J.J.Kolumban, On the Ulam-Hyers stability of first order differential systems with nonlocal initial conditions, Nonlinear Anal. Theory Methods Appl., 82 (2013),1-11.
  6. [6] M. Benchohra, J. E. Lazreg, Existence and unqiueness results for nonlinear implicit fractional differential equations with boundary conditions, Romanian Journal of Mathematics and Computer science, 4 (2014), 60-72.
  7. [7] P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Compositions of Hadamard-type fractional integration operators and the semigroup property, J. Math. Anal. Appl., 269(2) (2002), 387-400.
  8. [8] P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Mellin transform analysis and integration by parts for Hadamard-type fractional integrals, J. Math. Anal. Appl., 270(1) (2002), 1-15.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Publication Date

October 15, 2019

Submission Date

May 8, 2018

Acceptance Date

June 12, 2019

Published in Issue

Year 2019 Volume: 7 Number: 2

APA
Vivek, D., Kanagarajan, K., & Elsayed, E. (2019). Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations with Boundary Conditions. Konuralp Journal of Mathematics, 7(2), 279-287. https://izlik.org/JA64RD46XD
AMA
1.Vivek D, Kanagarajan K, Elsayed E. Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations with Boundary Conditions. Konuralp J. Math. 2019;7(2):279-287. https://izlik.org/JA64RD46XD
Chicago
Vivek, D., K. Kanagarajan, and Elsayed Elsayed. 2019. “Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations With Boundary Conditions”. Konuralp Journal of Mathematics 7 (2): 279-87. https://izlik.org/JA64RD46XD.
EndNote
Vivek D, Kanagarajan K, Elsayed E (October 1, 2019) Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations with Boundary Conditions. Konuralp Journal of Mathematics 7 2 279–287.
IEEE
[1]D. Vivek, K. Kanagarajan, and E. Elsayed, “Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations with Boundary Conditions”, Konuralp J. Math., vol. 7, no. 2, pp. 279–287, Oct. 2019, [Online]. Available: https://izlik.org/JA64RD46XD
ISNAD
Vivek, D. - Kanagarajan, K. - Elsayed, Elsayed. “Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations With Boundary Conditions”. Konuralp Journal of Mathematics 7/2 (October 1, 2019): 279-287. https://izlik.org/JA64RD46XD.
JAMA
1.Vivek D, Kanagarajan K, Elsayed E. Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations with Boundary Conditions. Konuralp J. Math. 2019;7:279–287.
MLA
Vivek, D., et al. “Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations With Boundary Conditions”. Konuralp Journal of Mathematics, vol. 7, no. 2, Oct. 2019, pp. 279-87, https://izlik.org/JA64RD46XD.
Vancouver
1.D. Vivek, K. Kanagarajan, Elsayed Elsayed. Stability Theory and the Existence of Hilfer Type Fractional Implicit Differential Equations with Boundary Conditions. Konuralp J. Math. [Internet]. 2019 Oct. 1;7(2):279-87. Available from: https://izlik.org/JA64RD46XD
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