**REFERENCES**

[1] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, 2000.

[2] K. B. Oldham, Fractional differential equations in electrochemistry, Advances in

Engineering Software, 41, (2010) 9-12.

[3] R. L. Magin, Fractional calculus models of complex dynamics in biological tissues,

Computers and Mathematics with Applications, 59, (2010) 1586-1593.

[4] M. D. Ortigueira, Fractional Calculus for Scientists and Engineers, Springer, 2011.

[5] J. Singh, D. Kumar, J. J. Nieto, Analysis of an el nino-southern oscillation model

with a new fractional derivative, Chaos, Solitons and Fractals, 99, (2017) 109– 115.

[6] Y. Tian, J. J. Nieto, The applications of critical-point theory discontinuous

fractional-order differential equations, Proceedings of the Edinburgh Mathematical

Society, 2014, (2014) 1–31, DOI: 10.1017/S001309151600050X.

[7] J. J. Nieto, Solvability of an implicit fractional integral equation via a measure

of noncompactness argument, Acta Mathematica Scientia, 37, (2017) 195–204.

[8] X. Gao, J. Yu, Chaos in the fractional order periodically forced complex Duffing

oscillators, Chaos, Solitons and Fractals, 24, (2005) 1097–1104.

[9] J. R. Wanga, Y. Zhoub, M. Feckan, Nonlinear impulsive problems for fractional

differential equations and Ulam stability, Computers and Mathematics with Applications,

64, (2012) 3389–3405.

[10] Z. M. Odibat, Analytic study on linear systems of fractional differential equations,

Computers and Mathematics with Applications, 59, (2010) 1171–1183.

[11] Bashir Ahmada, S. Sivasundaram, Dynamics and stability of impulsive hybrid

setvalued integro-differential equations with delay, Nonlinear Analysis, 65, (2006)

2082–2093.

[12] S. Abbas, E. Alaidarous, M. Benchohra, J. J. Nieto, Existence and stability of

solutions for Hadamard-Stieltjes fractional integral equations, Discrete Dynamics

in Nature and Society, 2015, (2015) DOI: 10.1155/2015/317094.

[13] M. D. la Sen, Total stability properties based on fixed point theory for a class

of hybrid dynamic systems, Fixed Point Theory and Applications, 2009 (2009)

DOI: 10.1155/2009/826438.

[14] J. O. Alzabut, J. J. Nieto, G. Tr. Stamov, Existence and exponential stability of

positive almost periodic solutions for a model of hematopoiesis, Boundary Value

Problems, 2009 (2009) DOI: 10.1155/2009/127510.

[15] G. M. Zaslavsky, A. A. Stanislavsky, M. Edelman, Chaotic and pseudochaotic

attractors of perturbed fractional oscillator, Chaos 16, (2006) 013102.

[16] E. Ahmed, A. M. A. El-Sayed, H. A. A. El-Saka, Equilibrium points, stability and

numerical solutions of fractional-order predatorprey and rabies models, Journal

of Mathematical Analysis and Applications, 325, (2007) 542–553.

[17] T.A. Burton, B. Zhang, Fractional equations and generalizations of Schaefers

and Krasnoselskiis fixed point theorems, Nonlinear Analysis: Theory, Methods

and Applications, 75, (2012) 6485–6495.

[18] F. Ge, C. Kou, Stability analysis by Krasnoselskii’s fixed point theorem for nonlinear

fractional differential equations, Applied Mathematics and Computation,

257, (2015) 308–316.

[19] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.

[20] M. Concezzi, R. Spigler, Some analytical and numerical properties of the MittagLeffler

functions, Fractional Calculus and Applied Analysis 18, (2015) 64-94.

[21] D. Qian, C. Li, R. P. Agarwal, P. J. Wong, Stability analysis of fractional differential

system with Riemann-Liouville derivative, Mathematical and Computer

Modelling, 52, (2010) 862–874.