Investigation of an implicit Hadamard fractional differential equation with Riemann-Stieltjes integral boundary condition

References

[1] ABBAS, M. I. — RAGUSA, M. A.: Solvability of Langevin equations with two Hadamard fractional derivatives via Mittag-Leffler functions, Appl. Anal. 101(9) (2022), 3231–3245.10.1080/00036811.2020.1839645Search in Google Scholar

[2] ABBAS, M. I.: On the Hadamard and Riemann-Liouville fractional neutral functional integrodifferential equations with finite delay, J. Pseudo-Differ. Oper. Appl. 10(2) (2019), 1–10.10.1007/s11868-018-0244-1Search in Google Scholar

[3] ABBAS, M. I.: Ulam stability of fractional impulsive differential equations with Riemann-Liouville integral boundary conditions, J. Contemp. Math. Anal. 50(5) (2015), 209–219.10.3103/S1068362315050015Search in Google Scholar

[4] ABBAS, M. I.: Existence and uniqueness of solution for a boundary value problem of fractional order involving two Caputo’s fractional derivatives, Adv. Differ. Eq. 2015 (2015), Art. ID 252.10.1186/s13662-015-0581-9Search in Google Scholar

[5] AHMAD, B. — ALGHANMI, M. — NTOUYAS, S. K. — ALSAEDI, A.: Fractional differential equations involving generalized derivative with Stieltjes and fractional integral boundary conditions, Appl. Math. Lett. 84 (2018), 111–117.10.1016/j.aml.2018.04.024Search in Google Scholar

[6] AHMAD, B. — NTOUYAS, S. K.: On Hadamard fractional integro-differential boundary value problems, J. Appl. Math. Comput. 47 (2015), 119–131.10.1007/s12190-014-0765-6Search in Google Scholar

[7] BENCHOHRA, M. — BOURIAH, S. — LAZREG, J. E. — NIETO, J. J.: Nonlinear implicit Hadamard’s fractional differential equations with delay in Banach space, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. Mathematica 55(1) (2016), 15–26.Search in Google Scholar

[8] BUTZER, P. L. — KILBAS, A. A. — TRUJILLO, J. J.: Compositions of Hadamard-type fractional integration operators and the semigroup property, J. Math. Anal. Appl. 269 (2002), 387–400.10.1016/S0022-247X(02)00049-5Search in Google Scholar

[9] BUTZER, P. L. — KILBAS, A. A. — TRUJILLO, J. J.: Fractional calculus in the Mellin setting and Hadamard-type fractional integrals, J. Math. Anal. Appl. 269 (2002), 1–27.10.1016/S0022-247X(02)00001-XSearch in Google Scholar

[10] BUTZER, P. L. — KILBAS, A. A. — TRUJILLO, J. J.: Mellin transform analysis and integration by parts for Hadamard-type fractional integrals, J. Math. Anal. Appl. 270 (2002), 1–15.10.1016/S0022-247X(02)00066-5Search in Google Scholar

[11] EL-SAYED, A. M. A. — GAAFAR, F. M.: Positive solutions of singular Hadamard-type fractional differential equations with infinite-point boundary conditions or integral boundary conditions, Adv. Differ. Eq. 2019 (2019), Art. ID 382.10.1186/s13662-019-2315-xSearch in Google Scholar

[12] GRANAS, A. — DUGUNDJI, J.: Fixed Point Theory, Springer-Verlag, New York, 2003.10.1007/978-0-387-21593-8Search in Google Scholar

[13] HADAMARD, J.: Essai sur l’etude des fonctions donnees par leur developpment de Taylor, J. Mat. Pure Appl. Ser. 8 (1892), 101–186.Search in Google Scholar

[14] KILBAS, A. A. — SRIVASTAVA H. M. — TRUJILLO, J. J.: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier Science B.V., Amsterdam, 2006.Search in Google Scholar

[15] LAKSHMIKANTHAM, V. — LEELA, S. — DEVI, J. V.: Theory of Fractional Dynamic Systems. Cambridge Scientific Publishers, 2009.Search in Google Scholar

[16] MILLER, K. S. — ROSS, B.: An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.Search in Google Scholar

[17] PODLUBNY, I.: Fractional Differential Equations, Academic Press, San Diego, 1999.Search in Google Scholar

[18] PONNUSAMY, S.: Foundations of Mathematical Analysis, Springer Science & Business Media, LLC, 2012.10.1007/978-0-8176-8292-7Search in Google Scholar

[19] PROTTER, M. H. — MORREY C. B. JR.: A First Course in Real Analysis, 2nd ed., Springer Science & Business Media, New York, 1991.10.1007/978-1-4419-8744-0Search in Google Scholar

[20] SAMKO, S. — KILBAS, A. A. — MARICHEV, O. L.: Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Longhorne, PA, 1993.Search in Google Scholar

[21] SMART, D. R.: Fixed Point Theorems, Cambridge University Press, Cambridge, 1980.Search in Google Scholar

[22] SONG, S. — CUI, Y.: Existence of solutions for integral boundary value problems of mixed fractional differential equations under resonance, Bound. Value Probl. 2020 (2020), Art. ID 23.10.1186/s13661-020-01332-5Search in Google Scholar

[23] ZHAI, C. — WANG, W.: Solutions for a system of Hadamard fractional differential equations with integral conditions, Num. Func. Ana. Optim. 41(2) (2020), 209–229.10.1080/01630563.2019.1620771Search in Google Scholar