REFERENCES
[1] S. 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.
ψ-FRACTIONAL DIFFERENTIAL EQUATIONS 413
[2] A.Arara, M.Benchohra, N.Hamidi, J.J.Nieto, Fractional order differential
equations on an unbounded domain, Nonlinear Anal. Theory Methods
Appl., 72, No. 2 (2010), 580-586.
[3] Z. Bai, H. Lu, Positive solutions for boundary value problem of nonlinear
fractional differential equation, J. Math. Anal. Appl., 311, No. 2 (2005), 495-505.
[4] C.S. Goodrich, Existence of a positive solution to a class of fractional
differential equations, Appl. Math. Lett., 23, (2010), 1050-1055.
[5] Z. Bai, H. Lu, Positive solutions for a boundary value problem of nonlinear
fractional differential equations, J. Math. Anal. Appl., 311 (2005), 495- 505.
[6] M. Benchohra, J. E. Lazreg, Existence and Uniqueness results for nonlinear
implicit fractional differential equations with boundary conditions,
Romanian Journal of Mathematics and Computer Science, 4, (2014), 60- 72.
[7] M. Benchohra, S. Bouriah, Existence and stability results for nonlinear
boundary value problem for implicit differential equations of fractional
order, Morccan J. Pure and Appl. Anal., 1, No. 1 (2015), 22-37.
[8] M. Benchohra, S. Hamani, S. K. Ntouyas, Boundary value problems for
differential equations with fractional order, Survey in Mathematics and
its Applications, 3 (2008), 1-12.
[9] R.Hilfer, Application of fractional Calculus in Physics, World Scientific,
Singapore, 1999.
[10] DH. Hyers, G. Isac, TM. Rassias, Stability of functional equation in several
variables, Vol. 34, Progress in nonlinea differential equations their
applications, Boston (MA): Birkhauser; 1998.
[11] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl.
Acad. Sci. , USA 27, (1941), 222-224.
[12] R. W. Ibrahim, Generalized Ulam-Hyers stability for fractional
differential equations, Int. J. Math., 23(2012), DOI:
10.1142/S0129167X12500565.
[13] S. M. Jung, Hyers-Ulam stability of linear differential equations of first
order, Appl. Math. Lett., 17(2004), 1135-1140.
[14] P. Muniyappan, S. Rajan, Hyers-Ulam-Rassias stability of fractional differential
equation, Int. J. Pure Appl. Math., 102, (2015), 631-642.
[15] Moustafa El-Shahed, Positive solutions for boundary value problem of
nonlinear fractional differential equation, Abstract and Applied Analysis
, 2007 (2007) Article ID 10368, 8 pages.
[16] I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
[17] Rabha W. Ibrahim, Ulam stability of boundary value problem, Kragujevac
Journal of Mathematics, 37(2) (2013), 287-297.
[18] Ricardo Almeida, A Caputo fractional derivative of a function with respect
to another function, Commun. nonlinear Sci. Numer. Simulat., 44,
(2017), 460-481.
[19] J. Vanterler da C. Sousa, E. Capelas de Oliveira, A Gronwall inequality
and the Cauchy-type problem by means of ψ-Hilfer operator, (2017).
https://www.researchgate.net/publication/319662380.
[20] S. G. Samko, A.A. Kilbas O. I. Marichev, Fractional Integrals and
Derivatives-Theory and Applications, Gordon and Breach Science Publishers,
Amsterdam , 1993.
[21] J. Wang, Y. Zhou, New concepts and results in stability of fractional differential
equations, Commun. nonlinear Sci. Numer. Simulat., 17 (2012),
2530-2538.