[1] Abbas, S., Benchohra, M., Lagreg, J.-E., Zhou, Y.: A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability. Chaos Solitons Fractals 102 (2017), 47-71. DOI 10.1016/j.chaos.2017.03.010 | MR 3671994 | Zbl 1374.34004

[2] Agarwal, R. P., Benchohra, M., Hamani, S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta. Appl. Math. 109 (2010), 973-1033. DOI 10.1007/s10440-008-9356-6 | MR 2596185 | Zbl 1198.26004

[3] Bagley, R. L., Torvik, P. J.: A different approach to the analysis of viscoelastically damped structures. AIAA J. 21 (1983), 741-748. DOI 10.2514/3.8142 | Zbl 0514.73048

[4] Bagley, R. L., Torvik, P. J.: A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol. 27 (1983), 201-210. DOI 10.1122/1.549724 | Zbl 0515.76012

[5] Bagley, R. L., Torvik, P. J.: On the appearance of the fractional derivative in the behavior of real material. J. Appl. Mech. 51 (1984), 294-298. DOI 10.1115/1.3167615 | Zbl 1203.74022

[6] Bhairat, S. P.: New approach to existence of solution of weighted Cauchy-type problem. Available at http://arxiv.org/abs/1808.03067 (2018), 10 pages.

[7] Bhairat, S. P., Dhaigude, D. B.: Existence and stability of fractional differential equations involving generalized Katugampola derivative. Available at https://arxiv.org/ abs/1709.08838 (2017), 15 pages.

[8] Chitalkar-Dhaigude, C. D., Bhairat, S. P., Dhaigude, D. B.: Solution of fractional differential equations involving Hilfer fractional derivative: Method of successive approximations. Bull. Marathwada Math. Soc. 18 (2017), 1-13.

[9] Dhaigude, D. B., Bhairat, S. P.: Existence and continuation of solutions of Hilfer fractional differential equations. Available at http://arxiv.org/abs/1704.02462v1 (2017), 18 pages. MR 3820828

[10] Dhaigude, D. B., Bhairat, S. P.: Existence and uniqueness of solution of Cauchy-type problem for Hilfer fractional differential equations. Commun. Appl. Anal. 22 (2017), 121-134. MR 3820828

[11] Dhaigude, D. B., Bhairat, S. P.: On existence and approximation of solution of nonlinear Hilfer fractional differential equations. (to appear) in Int. J. Pure Appl. Math. Available at http://arxiv.org/abs/1704.02464 (2017), 9 pages. MR 3820828

[12] Dhaigude, D. B., Bhairat, S. P.: Local existence and uniqueness of solutions for Hilfer-Hadamard fractional differential problem. Nonlinear Dyn. Syst. Theory 18 (2018), 144-153. MR 3820828

[13] Dhaigude, D. B., Bhairat, S. P.: Ulam stability for system of nonlinear implicit fractional differential equations. Progress in Nonlinear Dynamics and Chaos 6 (2018), 29-38. DOI 10.22457/pindac.v6n1a4

[14] Furati, K. M., Kassim, M. D., Tatar, N.-E.: Existence and uniqueness for a problem involving Hilfer fractional derivative. Comput. Math. Appl. 64 (2012), 1616-1626. DOI 10.1016/j.camwa.2012.01.009 | MR 2960788 | Zbl 1268.34013

[15] Furati, K. M., Tatar, N.-E.: An existence result for a nonlocal fractional differential problem. J. Fractional Calc. 26 (2004), 43-51. MR 2096756 | Zbl 1101.34001

[16] Gaafar, F. M.: Continuous and integrable solutions of a nonlinear Cauchy problem of fractional order with nonlocal conditions. J. Egypt. Math. Soc. 22 (2014), 341-347. DOI 10.1016/j.joems.2013.12.008 | MR 3260773 | Zbl 1306.34007

[17] Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, London (2000). DOI 10.1142/9789812817747 | MR 1890104 | Zbl 0998.26002

[18] Hilfer, R.: Experimental evidence for fractional time evolution in glass forming materials. Chemical Physics 284 (2002), 399-408. DOI 10.1016/S0301-0104(02)00670-5 | MR 1890106

[19] Kassim, M. D., Tatar, N.-E.: Well-posedness and stability for a differential problem with Hilfer-Hadamard fractional derivative. Abstr. Appl. Anal. 2013 (2013), Article ID 605029, 12 pages. DOI 10.1155/2013/605029 | MR 3139483

[20] Katugampola, U. N.: New approach to a generalized fractional integral. Appl. Math. Comput. 218 (2011), 860-865. DOI 10.1016/j.amc.2011.03.062 | MR 2831322 | Zbl 1231.26008

[21] Katugampola, U. N.: A new approach to generalized fractional derivatives. Bull. Math. Anal. Appl. 6 (2014), 1-15. MR 3298307 | Zbl 1317.26008

[22] Katugampola, U. N.: Existence and uniqueness results for a class of generalized fractional differenital equations. Available at https://arxiv.org/abs/1411.5229 (2016).

[23] Kilbas, A. A., Srivastava, H. M., Trujillo, J. J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies 204. Elsevier, Amsterdam (2006). DOI 10.1016/s0304-0208(06)x8001-5 | MR 2218073 | Zbl 1092.45003

[24] Mainardi, F.: Fractional Calculus and Waves in Linear Viscoelastisity. An Introduction to Mathematical Models. World Scientific, Hackensack (2010). DOI 10.1142/9781848163300 | MR 2676137 | Zbl 1210.26004

[25] Oliveira, D. S., Oliveira, E. Capelas de: Hilfer-Katugampola fractional derivative. Available at https://arxiv.org/abs/1705.07733 (2017). MR 3826051

[26] Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Mathematics in Science and Engineering 198. Academic Press, San Diego (1999). MR 1658022 | Zbl 0924.34008

[27] Salamooni, A. Y. A., Pawar, D. D.: Hilfer-Hadamard-type fractional differential equation with Cauchy-type problem. Available at https://arxiv.org/abs/1802.07483 (2018), 18 pages.

[28] Wang, J., Zhang, Y.: Nonlocal initial value problems for differential equations with Hilfer fractional derivative. Appl. Math. Comput. 266 (2015), 850-859. DOI 10.1016/j.amc.2015.05.144 | MR 3377602