УДК 517.9: 519.6

В.М. БУЛАВАЦЬКИЙ
Інститут кібернетики ім. В.М. Глушкова НАН України, Київ, Україна,
 v_bulav@ukr.net

ЗАДАЧА З КІНЦЕВОЮ ІНТЕГРАЛЬНОЮ УМОВОЮ
ДЛЯ ОДНОГО НЕЛІНІЙНОГО ДРОБОВО-ДИФЕРЕНЦІАЛЬНОГО
РІВНЯННЯ З БІПОРЯДКОВОЮ ПОХІДНОЮ ХІЛЬФЕРА–АДАМАРА

СПИСОК ЛІТЕРАТУРИ

• 1. Gao Z., Yu X. Existence results for BVP of a class of Hilfer fractional differential equations. Journ. Appl. Math. Comput. 2018. Vol. 56, N 1–2. P. 217–233.


• 2. Harikrishnan S., Kanagarajan K., Elsayed E.M. Existence of solutions of nonlocal initial value problems for differential equations with Hilfer–Katugampola fractional derivative. 2019. https://doi.org/10.1007/ .


• 3. Vivek D., Elsayed E.M., Kanagarajan K. Analytic study on boundary value problem of implicit differential equations via composite fractional derivative. Acta Mathematica Vietnamica. 2021. Vol. 46. P. 531–543.


• 4. Benchohra M., Bourian S., Nieto J. Boundary value problem for differential equations with generalized Hilfer-type fractional derivative. Fixed Point Theory. 2021. Vol. 22, N 2. P. 527–542.


• 5. Almalahi M.A., Abdo M.S., Panchal S.K. Periodic boundary value problems for fractional implicit differential equations involving Hilfer fractional derivative. Probl. Anal. Issues Anal. 2020. Vol. 9(27), N 2. P. 16–44.


• 6. Kassim M.D., Tatar N.-E. Well-posedness and stability for a differential problem with Hilfer–Hadamard fractional derivative. Abstract and Applied Analysis. 2013. Vol. 2013, article ID 605029. P. 1–12. https//doi.org/101155/ .


• 7. Vivek D., Kanagarajan K., Elsayed E.M. Nonlocal initial problems for differential equations with Hilfer–Hadamard fractional derivative. Nonlinear Analysis: Modelling and Control. 2018. Vol. 23, N 3. P. 341–360.


• 8. Vivek D., Kanagarajan K., Sivasundaram S. On the behavior of solutions of Hilfer–Hadamard type fractional neutral pantograph equations with boundary conditions. Communic. Appl. Analysis. 2018. N 2. P. 211–232.


• 9. Vivek D., Kanagarajan K., Elsayed E.M. A study of fractional integro-differential equations via Hilfer–Hadamard fractional derivative. General Mathematics. 2019. Vol. 27, N 1. P. 71–84.


• 10. Promsakon C., Ntouyas S.K., Tariboon J. Hilfer–Hadamard nonlocal integro-multipoint fractional boundary value problems. Journal of Function Spaces. 2021, article ID 8031524. P. 1–9. https//doi.org/10.1155/ .


• 11. Salamooni Ahmad Y.A., Pawar D.D. Existence and uniqueness of generalized fractional Cauchy-type problem. Universal Journal of Mathematics and Applications. 2020. Vol. 3, N 3. P. 121–128.


• 12. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations. Amsterdam: Elsevier, 2006. 523 p.


• 13. Bulavatsky V.M. Closed form of the solutions of some boundary-value problems for anomalous diffusion equation with Hilfer’s generalized derivative. Cybernetics and Systems Analysis. 2014. Vol. 50, N 4. P. 570–577.


• 14. Kolmogorov A.N., Fomin S.V. Elements of the theory of functions and functional analysis (in Russians). Moskow: Nauka, 1976. 496 p.


• 15. Granas A., Dugudji J. Fixed point theory. New York: Springer, 2003. 690 p.


• 16. Almalahi M.A., Panchal S.K. Existence and stability results of relaxation fractional differential equations with Hilfer–Katugampola fractional derivative. Adv. Theory Nonlin. Anal. Appl. 2020. Vol. 4, N 4. P. 299–315.


• 17. Harikrishnan S., Kanagarajan K., Vivek D. Some existence and stability results for integro-differential equations by Hilfer–Katugampola fractional derivative. Palestine Journal of Mathematics. 2020. Vol. 9(1). P. 254–262.


• 18. Abbas S., Benchohra M., Sivasundaram S. Dynamics and Ulam stability for Hilfer-type fractional differential equations. Nonlinear Stud. 2016. Vol. 23, N 4. P. 627–637.


• 19. Wang J., Zhou Y., Medved M. Existence and stability of fractional differential equations with Hadamard derivative. Topol. Methods in Nonlinear Anal. 2013. Vol. 41, N 1. P. 113–133.


• 20. Ye H., Gao J., Ding Y. A generalized Gronwall inequality and its application to a fractional differential equation. J. Math. Anal. Approx. Theory. 2007. Vol. 328. P. 1075–1081.


• 21. Gorenflo R., Kilbas A.A., Mainardi F., Rogosin S.V. Mittag-Leffler functions, related topics and applications. Berlin: Springer-Verlag, 2014. 454 p.