References
- S. Naz, M.N. Naeem, On the generalization of κ-fractional Hilfer-Katugampola derivative with Cauchy problem, Turk. J. Math., 45, (2021), 110–124.
- Y.C. Kwun, G. Farid, W. Nazeer; S. Ullah, S.M. Kang, Generalized Riemann-Liouville k-fractional integrals associated with Ostrowski type inequalities and error bounds of Hadamard inequalities, IEEE Access, 6, (2018), 64946–64953.
- K.D. Kucche, A.D. Mali, On the nonlinear (k, ψ )-Hilfer fractional differential equations, Chaos Solitons Fractals, 152, (2021), 111335.
- G.A. Dorrego, An alternative definition for the k-Riemann-Liouville fractional derivative, Appl. Math. Sci., 9, (2015), 481–491.
- R. Diaz, E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 2, (2007), 179–192.
- S. Mubeen, G.M. Habibullah, kfractional integrals and applications, Int. J. Contemp. Math. Sci., 7, (2012), 89–94.
- D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20, (1969), 458–464.
- Tariboon, J., Samadi, A., Ntouyas, S.K. Multi-point boundary value problems for (k, ˚)-Hilfer fractional differential equations and inclusions, Axioms, 11, (2022), 110.
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, (2000).
- R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci.Numer. Simul., 44, (2017), 460–481.
- R. Almeida, A.B. Malinowska, M. Teresa, T. Monteiro, Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications, Math. Methods Appl. Sci., 41(1), (2018), 336–352.
- F. Jarad, T. Abdeljawad, Generalized fractional derivatives and Laplace transform, Discrete Contin. Dyn. Syst., 13(3), (2020), 709–722.
- S. Hamani, M. Benchohra, John R. Graef, Existence results for boundary value problems with nonlinear fractional inclusions and integral conditions,Electron. J. Diff. Equ., 2010(20), (2010), 1–16.
- M. Benchohra, J. R. Graef, S. Hamani, Existence results for boundary value problems with nonlinear fractional differential equations, Appl. Anal., 87, (2008), 851–863.
- S. Belmor, C. Ravichandran, F. Jarad, Nonlinear generalized fractional differential equations with generalized fractional integral conditions, J. Taibah Univ. Sci., 14(1), (2020), 114–123.
- S. Belmor, F. Jarad, T. Abdeljawad, M.A. Alqudah, On fractional differential inclusion problems involving fractional order derivative with respect to another function. Fractals, 20(8),(2020), 2040002.
- S. B. Nadler, Multivalued contraction mappings, Pacific J. Math., 30, (1969) 475–88.
- T. Abdeljawad, F. Madjidi, F. Jarad, N. Sene, On dynamic systems in the frame of singular function dependent kernel fractional derivatives,Mathematics, 7(10), (2019), 946.
- R. Ameen, F. Jarad, T. Abdeljawad, Ulam stability for delay fractional differential equations with a generalized Caputo derivative, Filomat, 32(15), (2018), 5265–5274.
- F. Jarad, S. Harikrishnan, K. Shah, K. Kanagarajan, Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative, Discrete Contin. Dyn. Syst., 13(3), (2020) 723–739.
- B. Samet, H. Aydi, Lyapunov-type inequalities for an anti-periodic fractional boundary value problem involving -Caputo fractional derivative, J.Inequal. Appl., 2018(286), (2018), 9.
- J. Sousa, C. Vanterler da, K. D. Kucche, E. C. De Oliveira, Stability of ψ-Hilfer impulsive fractional differential equations, Appl. Math. Lett., 88, (2019), 73–80.
- J. Vanterler da C. Sousa, E. Capelas de Oliveira, Leibniz type rule: ψ-Hilfer fractional operator, Communications in Nonlinear Science and Numerical Simulation, 77, (2019), 305-311.
- D.S. Oliveira, E. Capelas de Oliveira, On a Caputo-type fractional derivative, Advances in Pure and Applied Mathematics, 10(2), (2019), 81–91
- J.V.C. Sousa, E.C. De Oliveira, On the ψ-Hilfer fractional derivative, Communications in Nonlinear Science and Numerical Simulation, 60, (2018), 72-91.
- I. Podlubny, Fractional differential equations, Academic Press, (1999).
- A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Di erential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, (2006).
- E. Mittal, S. Joshi, Note on k-generalized fractional derivative, Discret. Contin. Dyn. Syst., 13, (2020), 797–804.
- S.K. Magar, P.V. Dole, K.P. Ghadle, Pranhakar and Hilfer-Prabhakar fractional derivatives in the setting of y-fractional calculus and its applications, Krak. J. Math., 48, 2024, 515–533.
- P. Agarwal, J. Tariboon, S.K. Ntouyas, Some generalized Riemann-Liouville k-fractional integral inequalities, J. Ineq. Appl., 2016, (2016), 122.
- G. Farid, A. Javed, A.U. Rehman, On Hadamard inequalities for n-times differentiable functions which are relative convex via Caputo k-fractional derivatives, Nonlinear Anal. Forum, 22, (2017), 17–28.
- M.K. Azam, G. Farid, M.A. Rehman, Study of generalized type k-fractional derivatives, Adv. Differ. Equ., 2017, (2017), 249.
- L.G. Romero, L.L. Luque, G.A. Dorrego, R.A. Cerutti, On the k-Riemann-Liouville fractional derivative, Int. J. Contemp. Math. Sci., 8, (2013), 41–51.