Rodrigo Ponce C.

Publications:

1. Periodic solutions of degenerate differential equations in vector-valued function spaces, Joint work with C. Lizama. Studia Math., 202 (2011), 49-63. More
2. Bounded solutions to a class of semilinear integro-differential equations in Banach spaces, Joint work with C. Lizama. Nonlinear Anal., 74 (2011) 3397-3406. More
3. Almost automorphic solutions to abstract Volterra equations on the line, Joint work with C. Lizama. Nonlinear Anal., 74 (2011) 3805-3814. More
4. Maximal Regularity for Perturbed Integral Equations on the Line, Joint work with C. Lizama. Integral Equations Operator Theory 74 (2012), no. 4, 513-526. More
5. Bounded mild solutions to fractional integro-differential equations in Banach spaces, Semigroup Forum, 87, (2013), 377-392, DOI 10.1007/s00233-013-9474-y. More
6. Hölder continuous solutions for fractional differential equations and maximal regularity, J. of Differential Equations, 255 (2013), 3284-3304. More
7. Maximal regularity for degenerate differential equations with infinite delay in periodic vector-valued function spaces, Joint work with C. Lizama. Proc. Edin. Math. Soc. 56 (2013), no. 3, 853-871. More
8. Hölder continuous solutions for Sobolev type differential equations, Math. Nachr. 287, No. 1, 70-78 (2014), DOI 10.1002/mana.201200168. More
9. A connection between almost periodic functions defined on time scales and R, with C. Lizama and J. G. Mesquita. Appl. Anal., (2014), DOI 10.1080/00036811.2013.875161. More
10. On the boundedness of generalized Cèsaro operators on Sobolev spaces, Joint work with C. Lizama, P.J. Miana and L. Sánchez-LaJusticia. J. Math. Anal. Appl. 419 (2014), no. 1, 373-394. More
11. On $C^\alpha$-Hölder classical solutions for non-autonomous neutral differential equations: the nonlinear case, Joint work with E. Hernández and D. O'Regan. J. Math. Anal. Appl. 420 (2014), no. 2, 1814-1831. More
12. Weighted pseudo almost automorphic solutions to a semilinear fractional differential equation with Stepanov-like weighted pseudo almost automorphic nonlinear term, Joint work with Y. K. Chang and Mei-Juan Zhang. Applied Math. and Computation, 257 (2015) 158-168. More
13. Weighted pseudo antiperiodic solutions for fractional integro-differential equations in Banach spaces, Joint work with E. Álvarez and C. Lizama. Applied Math. and Computation, 259 (2015) 164-172. More
14. On the compactness of fractional resolvent families, Joint work with C. Lizama and A. Pereira. Semigroup Forum, (2016), DOI 10.1007/s00233-016-9788-7. More
15. Existence of mild solutions to nonlocal fractional Cauchy problems via compactness, Abstract and Applied Analysis, (2016), Article ID 4567092. More
16. Maximal $L^p$-regularity for fractional differential equations on the line. Joint work with V. Poblete. Math. Narch. 290, No. 13, 2009-2023 (2017), DOI 10.1002/mana.201600175. More
17. On the well-posedness of degenerate fractional differential equations in vector valued function spaces, Israel J. of Math. 219, (2017) 727-755. More
18. Almost automorphic solutions of Volterra equations on time scales. Joint work with C. Lizama, with J.G. Mesquita and E. Toon, Differential and Integral Equations, 30 (2017), 667-694. More
19. Approximate controllability for fractional differential equations of Sobolev type via properties on resolvent operators. Joint work with Y. K. Chang and A. Pereira. Fractional Calculus and Applied Analysis, 20, (2017), 963-987. More
20. Norm continuity for strongly continuous families of operators. Joint work with C. Lizama and A. Pereira. International Journal of Evolution Equations 10, (2017), 145-162. More
21. Properties of solution sets for Sobolev type fractional differential inclusions via resolvent family of operators. Joint work with Y. K. Chang. Eur. Phys. J. Special Topics 226, (2017), 3391-3409. https://doi.org/10.1140/epjst/e2018-00015-y. More
22. Discrete-time theorems for global and pointwise dichotomies of cocycles over semiflows. Joint work with F. Bataran and C. Preda. Monatshefte fur Mathematik, 186 (2018), no. 4, 579-607. More
23. Well-posedness, regularity, and asymptotic behavior of the continuous and discrete solutions of linear fractional integro-differential equations with order varying in time. Joint work with E. Cuesta. Electronic J. of Differential Equations, Vol. 2018, 173, (2018), 1-27. More
24. Uniform exponential stability and its applications to bounded solutions of integro-differential equations in Banach spaces. Joint work with Y. K. Chang. J. Integral Equations and Applications, 30 (2018), no. 3, 347-369. More
25. Existence and optimal controls for fractional stochastic evolution equations of Sobolev type via fractional resolvent operators. Joint work with Y. K. Chang and Y. Pei. Journal of Optimization Theory and Applications, 182 (2019), no. 2, 558-572. More
26. Sobolev type time fractional differential equations and optimal controls with the order in $(1,2).$ Joint work with Y. K. Chang. Differential Integral Equations 32 (2019), no. 9-10, 517-540. More
27. Fractional differential equations of Sobolev type with sectorial operators. Joint work with Y. K. Chang and S. Rueda. Semigroup Forum 99 (2019), no. 3, 591-606. More
28. Asymptotic behavior of mild solutions to fractional Cauchy problems in Banach spaces. Appl. Math. Lett. 105 (2020), 106322. More
29. Mild solutions to integro-differential equations in Banach spaces. Journal of Differential Equations, (2020), 269, 180-200. More
30. Time discretization of fractional subdiffusion equations via fractional resolvent operators. Computers and Mathematics with Applications 80 (2020), no. 4, 69-92. More
31. Subordination Principle for fractional diffusion-wave of Sobolev type. Fract. Calc. Appl. Anal. 23 (2020), no. 2, 427-449. More
32. Bounded solutions to functional integro-differential equations arising from heat conduction in materials with memory. Joint work with J. Alzabut and Y. K. Chang. Journal of Mathematical Sciences, (2020), DOI:https://doi.org/10.36535/0233-6723-2020-178-41-56. More
33. Solvability of fractional differential inclusions with nonlocal initial conditions via resolvent family of operators. Joint work with Y. K. Chang and X. S. Yang. Int. Journal of Nonlinear Sciences and Numerical Simulation, (2020), DOI: https://doi.org/10.1515/ijnsns-2019-0210. More
34. A subordination principle for subdiffusion equations with memory. J. of Integral Equations and Applications, 2020, Volume 32 (2020), No. 4, 479-493, DOI: 10.1216/jie.2020.32.479. More
35. Solutions of abstract integro-differential equations via Poisson transformation. Joint work with C. Lizama. Mathematical Methods in the Applied Sciences, (2021), 44(3), pp. 2495-2505. https://doi.org/10.1002/mma.6042. More
36. Mild solutions for a multi-term fractional differential equation via resolvent operators. Joint work with Y. K. Chang. AIMS-Mathematics, 2021, Volume 6, Issue 3: 2398-2417. https://doi.org/10.3934/math.2021146. More
37. Asymptotic behavior and representation of solutions to a Volterra kind of equation with a singular kernel. Joint work with M. Warma. Semigroup Forum, 102, 250-273 (2021). https://doi.org/10.1007/s00233-020-10157-8. More
38. Hölder regularity for abstract semi-linear fractional differential equations in Banach spaces. Joint work with E. Cuesta. Computers and Mathematics with Applications, (2021), 85 (2021), 57-68. https://doi.org/10.1016/j.camwa.2021.01.010. More
39. Discrete subdiffusion equations with memory. Applied Mathematics and Optimization, 84 (2021), no. 3, 3475-3497. https://doi.org/10.1007/s00245-021-09753-z. More
40. Explicit representation of discrete fractional resolvent families in Banach spaces. Joint work with J. González-Camus. Fract. Calc. Appl. Anal., Vol. 24, No 6 (2021), pp. 1853--1878. More
41. Abstract fractional linear pseudo-parabolic equations in Banach spaces. Well-posedness, regularity, and asymptotic behavior. Joint work with E. Cuesta. Fract. Calc. Appl. Anal., Vol. 25, No 6 (2022), pp. 2332--2355. More
42. Well-Posedness of second order differential equations with memory. Math. Nachr., Vol. 295, No. 11, (2022), 2246-2264 DOI: 10.1002/mana.202000113. More
43. Time discretization and convergence to superdiffusion equations via Poisson distribution. Joint work with C. Lizama. Commun. Pure Appl. Anal., Vol. 22, No. 2, 572-596, (2023). More
44. Cosine and sine families on time scales and abstract nonlinear second order dynamic equations on time scales. Math. Methods in Appl. Sciences, Vol. 46, No. 4 3923-3936, (2023), DOI:10.1002/mma.8729. More
45. Discretization of C0-semigroups and discrete semigroups of operators in Banach spaces. Math. Methods in Appl. Sciences, Vol. 46, No. 8, 9378-9390, (2023). More
46. Properties of vector-valued t-discrete fractional calculus and its connection with Caputo fractional derivatives. Joint work with Y. K. Chang. Constr. Approx., Vol. 57, No. 3, 1133-1144, (2023). More
47. Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation. Joint work with H. Antil, U. Biccari, M. Warma and S. Zamorano, Evol. Equ. Control Theory 13 (2024), no. 3, 893-924. DOI:10.3934/eect.2024010, (2024). More
48. Periodic solutions to second-order differential equations with fading memory. Math. Z. 307 (2024), no. 1, Paper No. 5, 19 pp. More
49. Identification of the order in fractional discrete systems. Math. Methods in Appl. Sciences. Math. Methods Appl. Sci. 47 (2024), no. 12, 9758-9768. More
50. Approximate controllability of abstract discrete fractional systems of order $1<\alpha<2$ via resolvent sequences. J. of Optimization Theory and Applications. To appear, (2024). More
Existence of solutions for abstract nonlinear fractional differential equations. Joint work with D. O'Regan and E. Hernandez. Submitted.
Abstract cosine and sine functions on time scales and applications to abstract Cauchy problems. Joint work with J. G. Mesquita and A. Pereira. Submitted.

Book:

Publications in Math Education:

1. Una lección sobre el Teorema de Thales vista desde el conocimiento especializado del profesor. Joint work with J. Carrillo, N. Climent, G. Espinoza and C. Henríquez. Revista Educación Matemática, 33-1, (2021), 98-124, https://doi.org/10.24844/EM3301.04.
2. Trabajo matemático de un profesor basado en tareas y ejemplos propuestos para la enseñanza. Joint work with J. Carrillo, N. Climent, G. Espinoza and C. Henríquez. Enseñanza de las Ciencias, 39-2 (2021), 123-142, https://doi.org/10.5565/rev/ensciencias.3210.

Projects:

Fondecyt Grant 11130619: Stability of resolvent families and applications