Kragujevac Journal of Mathematics
University of Kragujevac - Faculty of Science

[1]   S. Abbas, M. Benchohra, J. Lagreg, A. Alsaedi and Y. Zhou, Existence and Ulam stability for fractional differential equations of Hilfer-Hadamard type, Adv. Difference Equ. 180 (2017), DOI 10.1186/s13662–017–1231–1.

[2]   B. Ahmad and S. K. Ntouyas, Initial value problem of fractional order Hadamard-type functional differential equations, Electron. J. Differential Equations 2015 (2015), 1–9.

[3]   A. O. Akdemir, A. Ekinci and E. Set, Conformable fractional integrals and related new integral inequalities, J. Nonlinear Convex Anal. 18 (2017), 661–674.

[4]   A. O. Akdemir, E. Set and A. Ekinci, On new conformable fractional integral inequalities for product of different kinds of convexity, TWMS Journal of Applied and Engineering Mathematics 9 (2019), 142–150.

[5]   R. Almeida, A. B. Malinowska and T. Odzijewicz, Fractional differential equations with dependence on the Caputo-Katugampola derivative, Journal of Computational and Nonlinear Dynamics 11 (2016), 11 pages.

[6]   M. Benchohra and J. E. Lazreg, On stability for nonlinear implicit fractional differential equations, Matematiche (Catania) 70 (2014), 49–61.

[7]   M. Benchohra and J. E. Lazreg, Existence and Ulam stability for nonlinear implicit fractional differential equations with Hadamard derivative, Stud. Univ. Babes-Bolyai Math. 62 (2017), 27–38.

[8]   D. B. Dhaigude and S. P. Bhairat, Existence and uniqueness of solution of Cauchy type problem for Hilfer fractional differential equations, Communications in Applied Analysis 22 (2018), 121–134.

[9]   D. B. Dhaigude and S. P. Bhairat, Existence and continuation of solutions of Hilfer fractional differential equations, J. Math. Model. 7 (2019), 1–20.

[10]   M. A. Dokuyucu, D. Baleanu and E. Celik, Analysis of the fractional Keller-Segel model, Filomat 32(16) (2018), 5633–5643.

[11]   M. A. Dokuyucu, E. Celik, H. Bulut and H. M. Baskonus, Cancer treatment model with the Caputo-Fabrizio fractional derivative, Eur. Phys. J. Plus 133 (2018), Paper ID 92, DOI 10.1140/epjp/i2018-11950-y.

[12]   A. Ekinci and N. Eroǧlu, New generalizations for convex functions via conformable fractional integrals, Filomat 33(14) (2019), 4525–4534.

[13]   A. Ekinci and M. E. Özdemir, Some new integral inequalities via Riemann-Liouville integral operators, Appl. Comput. Math. 3 (2019), 288–295.

[14]   K. M. Furati, M. D. Kassim and N. e-. Tatar, Existence and uniqueness for a problem involving Hilfer fractional derivative, Comput. Math. Appl. 64 (2012), 1616–1626.

[15]   K. M. Furati, M. D. Kassim and N. e-. Tatar, Non-existence of global solutions for a differential equations involving Hilfer fractional derivative, Electron. J. Differential Equations 2013 (2013), 1–10.

[16]   R. Hilfer, Fractional Time Evolution: Applications in Fractional Calculus in Physics, World Scientific, London, 2000.

[17]   R. Hilfer, Y. Luckho and Z. Tomovski, Operational method for the solution of fractional differential equations with generalized Riemann-Liouville fractional derivatives, Fract. Calc. Appl. Anal. 12 (2009), 289–318.

[18]   S. M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001.

[19]   M. D. Kassim, K. M. Furati and N. -E. Tatar, On a differential equation involving Hilfer-Hadamard fractional derivative, Abstr. Appl. Anal. 2012 (2012), Article ID 391062, 17 pages.

[20]   U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput. 218 (2011), 860–865.

[21]   U. N. Katugampola, A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl. 6 (2014), 1–15.

[22]   A. A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc. 38 (2001), 1191–1204.

[23]   C. Kou, H. Zhou and M. Medved, Existence and continuation theorems of Riemann-Liouville type fractional differential equations, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2011), Article ID 1250077, 12 pages.

[24]   K. D. Kucche and S. T. Sutar, Stability via successive approximation for nonlinear implicit fractional differential equations, Moroccan Journal of Pure and Applied Analysis 3 (2017), 36–55.

[25]   K. S. Miller and B. Ross, A Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.

[26]   I. Mumcu, E. Set and A. O. Akdemir, Hermite-Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals, Miskolc Math. Notes 20 (2019), 409–424.

[27]   D. S. Oliveira and E. C. de Oliveira, Hilfer-Katugampola fractional derivative, Comput. Appl. Math. 37 (2018), 3672–3690.

[28]   D. R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge, 1973.

[29]   R. Subashini, K. Jothimani, S. Saranya and C. Ravichandran, On the results of Hilfer fractional derivatives with nonlocal conditions, International Journal of Pure and Applied Mathematics 118 (2018), 277–289.

[30]   S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1968.

[31]   D. Vivek, K. Kanagrajan and E. M. Elsayed, Nonlocal initial value problems for implicit differential equations with Hilfer-Hadamard fractional derivative, Nonlinear Analysis: Modelling and Control 23 (2018), 341–360.

[32]   J. Wang and Y. Zhang, Nonlocal initial value problems for differential equations with Hilfer fractional derivative, Appl. Math. Comput. 266 (2015), 850–859.

[33]   J. Wang, Y. Zhou and M. Medved, Existence and stability of fractional differential equations with Hadamard derivative, Topol. Methods Nonlinear Anal. 41 (2013), 113–133.

[34]   H. Yaldiz and A. O. Akdemir, Katugampola fractional integrals within the class of convex functions, Turkish Journal of Science 3 (2018), 40–50.