1 |
J.B. Diaz, B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309.
DOI
|
2 |
V. Lakshmikantham, Theory of fractional functional differential equations, Nonlinear Anal. 69 (2008), 3337-3343.
DOI
|
3 |
K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equation, Wiley, New York, 1993.
|
4 |
P. Muniyappan, S. Rajan, Hyers-Ulam-Rassias stability of fractional differential equations, Internat. J. Pure Appl. Math. 102 (2015), 631-642.
|
5 |
P. Muniyappan, S. Rajan, Stbility of a class of fractional integro differential equation, Fixed Point Theory 20 (2019), 591-600.
DOI
|
6 |
S. Rajan, P. Muniyappan, C. Park, S. Yun, J.R. Lee, Stability of fractional differential equation with boundary conditions, J. Comp. Anal and Appl. 23-4 (2017), 750-757.
|
7 |
Th.M. Rassias, On the stability of linear mappig in Banach spaces, Proc. Amer. Soc. 72 (1978), 297-300.
DOI
|
8 |
P. Karthikeyan, Some results for boundary value problem of an integrodifferential equations with fractional order, Dynamic Systems and Applications 20 (2004), 17-24.
|
9 |
K. Diethelm, A.D. Freed, On the solution of nonlinear fractional order differential equation used in the modeling of viscoplasticity,in: F.keil, W.Maskens,H.Voss(Eds).Scientific computing in chemical Engineering II-Computational Fluid Dynamics and Molecular Properties, Springer-Verlag, Heideberg, 1999.
|
10 |
S.M. Jung, A fixed point approach to the stability of differential equations y'(t) = G(x,y), Bull. Malays. Math. Sci. Soc. 33 (2010), 47-56.
|
11 |
A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential equations, Elsevier, Amsterdam, 2006.
|
12 |
J. Klamka, Controllability of Dynamical Systems, Kluwer Academic, Dordrecht, 1993.
|
13 |
V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equation, Nonlinear Anal. 69 (2008), 2677-2682.
DOI
|
14 |
D. Baleanu, Z.B. Gunvenuc, J.A.T. Machdo, New Trends in Nenotechnology and Fractional Calculus Applications, Springer, Berlin, 2010.
|
15 |
A. Pazy, Semigroups of Linear operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
|
16 |
A. Vinodkumar, K. Malar, M. Gowrisankar, P. Mohankumar, Existence, uniqueness and stability of random impulsive fractional differential equations, Journal of Acta Mathematica Scientia 36 (2006), 428-442.
|
17 |
S. Zhang, Positive solutions for boundary value problems for nonlinear fractional differential equations, Elec. J. Diff. Eqn. 36 (2006), 1-12.
|
18 |
Y. Zhou, F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Comput. Math. Appl. 59 (2010), 1063-1077.
DOI
|
19 |
S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and derivatives, Theory and Applications, Gordon and Breach Yverden, 1993.
|
20 |
D. Tamizharasan, K. Karthikeyan, Controllability results for fractional integrodifferential systems with boundary conditions, Indian J. Pure Appl. Math. 52 (2021), 39-45.
DOI
|
21 |
D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, Singapore, 2012.
|
22 |
B. Bonilla, M. Rivero, L. Rodriguez-Germa, J.J. Trujillo, Fractional differential equations as alternative models to nonlinear differential equations, Applied Mathematics and Computation 86 (2007), 79-88.
|
23 |
L. Cadariu, V. Radu, Fixed points and the stability of Jensens functional equation, J. Inequal. Pure Appl. Math. 4 (2003).
|
24 |
D.R. Smart, Fixed point Theorems, Cambridge University Press, Cambridge 66, 1980.
|
25 |
W. Lin, Global existence theory and chaos control of fractional differential equation, J. Math. Anal. Appl. 332 (2007), 709-726.
DOI
|
26 |
P. Muniyappan, S. Rajan, Stability of a class of fractional integro-differential equation with nonlocal initial condition, Acta. Math. Univ. comenianae LXXXVII 1 (2018), 85-95.
|
27 |
I. Podlubny, Fractional Differential Equations, San Diego Academic Press, New York, 1999.
|
28 |
Y. Zhou, F. Jiao, F. Li, Existence and uniqueness for fractional neutral differential equations with infinite delay, Nonlinear Analysis 71 (2009), 3249-3256.
DOI
|
29 |
S.M. Ulam, Problems in Modern Mathematics, Rend. Chap.VI, Wiley, New York, 1940.
|
30 |
D.N. Chalishajar, K. Malar, R. Ilavarasi, Existence and Controllability Results of Impulsive Neutral Fractional Intergro-diferential Equations with Sectorial operator and Infinite Delay, Journal of Dynamics of Continuous, Discrete and Impulsive system series A: Mathematical Analysis 28 (2011), 77-106.
|
31 |
V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, Cambridge, 2009.
|
32 |
D. Baleanu, J.A. Tenreiro Machado, A.C.J. Luo, Fractional Dynamics and Control, Springer, Berlin, 2012.
|
33 |
D.H. Hyers, On the stability of the linear functional equations, Proc. Nat. Acad. Sci. 27 (1941), 222-224.
DOI
|
34 |
K. Karthikeyan, J.J. Trujillo, Existence and uniqueness results for fractional integrodifferential equations with boundary value conditions, Communications in Nonlinear Science and Numerical Simulation 17 (2012), 4037-4043.
DOI
|
35 |
A. Anguraj, A. Vinodkumar , K. Malar, Existence and Stability Results for Random Impulsive Fractional Pantograph Equations, Faculty of Sciences and Mathematics, University of Nis, Serbia, 2016, 3839-3854.
|
36 |
A. Anguraj, P. Karthikeyan, G.M. NGuerekata, Nonlocal Cauchy problem for some fractional abstract integrodifferential equations in Banach space, Commn. Math. Anal. 6 (2009), 1-6.
|
37 |
R.P. Agarwal, M. Benchohra, and S. Hamanani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math. 109 (2010), 973-1033.
DOI
|
38 |
M. Akkouchi, Hyers-Ulam-Rassias stability of nonlinear Volterra integral equations via a fixed point approach, Acta Univ. Apulensis Math. Inform. 26 (2011), 257-266.
|