___

• [1] A. Ahmadkhanlu, M. Jahanshahi, On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales, B. Iran. Math. Soc., 38, (2012), 241-252.[2] N. Benkhettou, A. Hammoudi, D. F. M. Torres, Existence and uniqueness of solution for a fractional Riemann-lioville initial value problem on time scales, Journal of King Saud University-Science, 28,(2016),87-92.[3] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkh˜auser, Boston, 2003.[4] M. Bohner, A. Peterson, Dtnamica equations on times scale, Birkhauser Boston, Boston, MA.[5] R.P. Agarwal, M. Bohner, Basic calculus on time scales and some of its applications, Results Math., 35, (1999), 3-22.[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] A. Granas, and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.[8] S. Harikrishnan, Kamal Shah, Dumitru Baleanu, K. Kanagarajan, Note on the solution of random differential equations via ψ-Hilfer fractional derivative, Advances in Difference Equations, 2018, 2018:224.[9] R. W. Ibrahim, Generalized Ulam-Hyers stability for fractional differential equations, Int. J. Math., 23,(2012).[10] V. Lupulescu, S.K. Ntouyas, Random fractional differential equations International electronic journal of pure and applied mathematics, 4(2), 2012, 119-136.[11] H. Gu, J.J. Trujillo, Existence of mild solution for evolution equation with Hilfer fractional derivative, Appl. Math. Comput., 15(2015), 344-354.[12] R.Hilfer, Application of fractional Calculus in Physics, World Scientific, Singapore, 1999.[13] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.[14] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Sci. Publishers, Yverdon, 1993.[15] T. T. Soong, Random Differential Equations in Science and Engineering. Academic Press, New York, 1973.[16] K.M. Kolwankar, A.D. Gangal, Fractional differentiability of nowhere differentiable functions and dimension, Chaos, 6 (1996) 505-513.[17] J. Vanterler da C. Sousa, E. Capelas de Oliveira, On the ψ-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul., In Press, Accepted Manuscript-2018.[18] J. Vanterler da C. Sousa, E. Capelas de Oliveira, Ulam-Hyers stability of a nonlinear fractional Volterra integro-differential equation, Appl. Math. Lett., Accepted Manuscript-2018.[19] J. Vanterler da C. Sousa, D. Santos Oliveira, E. Capelas de Oliveira, On the existence and stability for noninstantaneous impulsive fractional integrodifferential equation, Math. Meth. Appl. Sci., (2018) 113.[20] E. Capelas de Oliveira, J. Vanterler da C. Sousa, UlamHyersRassias stability for a class of fractional integro-differential equations, Results Math., (2018), 73:111.[21] J. Vanterler da C. Sousa, Kishor D. Kucche, E. Capelas de Oliveira, Stability of ψ-Hilfer impulsive fractional differential equations, Appl. Math. Lett., (2018).[22] D. Vivek, K. Kanagarajan, E.M. Elsayed, Some existence and stability results for Hilferfractional implicit differential equations with nonlocal conditions, Mediterr. J. Math., 15, (2018), 1-15.[23] H. Vu, Random fractional functional differential equations, International Journal of Nonlinear Analysis and Applications, 7(2), (2016), 253-267.[24] 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.