[1] M.S. Abdo, S.K. Panchal, Fractional integro-differential equations involving ψ− Hilfer fractional
derivative, Adv. Appl. Math. Mech. 11 (2019) 338–359.
[2] M.A. Almalahi, M.S. Abdo, S.K. Panchal ψ-Hilfer fractional functional differential equation by
Picard operator method, J. Appl. Nonlinear Dynam. 9 (2020) 685–702.
[3] R. Almeida, A Caputo fractional derivative of a function with respect to another function, Comm.
Nonlinear Sci. Numer. Sinulat., 44 (2017) 460–481.
[4] T.M. Atanackovic, S. Pilipovic, B. Stankovic, D. Zorica, Fractional calculus with applications in
mechanics: Vibrations and diffusion processes, Wiley-ISTE, London, Hoboken, 2014.
[5] S.P. Bhairat, Existence and continuation of solutions of Hilfer fractional differential equations, J.
Math. Model. 7 (2019) 1–20.
[6] S.P. Bhairat, On local existence of solution for nonlinear Hilfer fractional differential equation,
Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 29 (2022) 363–374.
[7] S.P. Bhairat, New approach to existence of solution for weighted Cauchy-type problem, J. Math.
Model. 8 (2020) 377–391.
[8] D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation,
J. Math. Anal. Appl. 204 (1996) 609–625.
[9] K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics,
Springer–Verlag Berlin Heidelberg, 2010.
[10] D.B. Dhaigude, S.P. Bhairat, Existence and uniqueness of solution of Cauchy-type problem for
Hilfer fractional differential equations, Comnun. Appl. Anal. 22 (2018) 121–134.
[11] D.B. Dhaigude, S.P. Bhairat, Local existence and uniqueness of solution of Hilfer fractional differ-
ential equations, Nonlinear Dyn. Syst. Theory. 18 (2018) 144–153.
[12] K.M. Furati, M.D. Kassim,Existence and uniqueness for a problem involving Hilfer fractional
derivative, Computer Math. Appl. 64 (2012) 1616–1626.
[13] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
[14] A.A. Kilbas, H.M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential
Equations, North-Holland Math Stud, 204 Elsevier, Amsterdam, 2006.
[15] K.D. Kucche, A.D. Mali, J. Vanterler da C. Sousa, On the nonlinear ψ-Hilfer fractional differential
equations, Comput. Appl. Math., 38 (2019) 73.
[16] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, an Introduction to Mathe-
matical Model, Imperical College Press, World Scientific Publishing, London, 2010.
[17] F. Norouzi, G.M. N’Guerekata A study of ψ−Hilfer fractional differential system with application
in financial crisis, Chaos Solitons Fractals 6 (2021) 100056.
[18] I. Podlubny, Fractional Differential Equations, Academic Press, 1998.
[19] A. Salim, M. Benchohra, J.R. Graef, J.E. Lazreg, Initial value problem for hybrid ψ-Hilfer frac-
tional implicit differential equations, J. Fixed Point Theory Appl. 24 (2022) 1–14.
[20] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives - Theory and Appli-
cations, Gordon and Breach, 1993.
[21] C. Sousa, E.C. de Oliveira, Leibniz type rule: ψ-Hilfer fractional operator, Comnun. Nonlinear
Sci. Numer. Sinulat. 77 (2019) 305–311.
[22] H.G. Sun, Y. Zhang, D. Baleanu, W. Chena, Y.Q. Chene, A new collection of real world applica-
tions of fractional calculus in science and engineering, Comnun. Nonlinear Sci. Numer. Sinulat. 64
(2018) 213–231.
[23] R. Toledo-Henrnandez, V. Rico-Ramirez, G.A. Iglesias-Silva, U.M. Diwekar, A fractional calculus
approach to the dynamic optimization of biological reactive systems. Part I: Fractional models for
biological reactions, Chem. Eng. Sci., 117 (2014) 217–228.
[24] J. Vanterler da C. Sousa, E. Capelas de Oliveira, On the ψHilfer fractional derivative, Comnun.
Nonlinear Sci. Numer. Sinulat. 60 (2018) 72–91.
[25] J. Vanterler da C. Sousa, E. Capelas Oliveira, A Gronwall inequality and the Cauchy-type problem
by means of ψ-Hilfer operator, Diff. Equ. Appl. 11 (2019), 87–106.
[26] N. Vieira, M.M. Rodregues, M. Ferriera, Fractional gradient methods via ψ−Hilfer derivative,
Fractal Fract. 7 (2023) 275.
[27] X. Yang and Y. Liu, Picard iterative processes for initial value problems of singular fractional
differential equations, Adv. Differ. Equat. 2014 (2014) 102.
)