Publications

Peer reviewed journals

1. R. A. C. Ferreira and D. F. M. Torres, Remarks on the calculus of variations on time scales, Int. J. Ecol. Econ. Stat. 9 (2007), no. F07, 65-73.

2. M. R. S. Ammi, R. A. C. Ferreira and D. F. M. Torres, Diamond-alpha Jensen's inequality on time scales, J. Inequal. Appl. 2008, Art. ID 576876, 13 pp.

3. R. A. C. Ferreira and D. F. M. Torres, Generalizations of Gronwall-Bihari inequalities on time scales, J. Difference Equ. Appl. 15 (2009), no. 6, 529-539.

4. R. A. C. Ferreira, M. R. Sidi Ammi and D. F. M. Torres, Diamond-alpha integral inequalities on time scales, Int. J. Math. Stat. 5 (2009), A09, 52-59.

5. R. A. C. Ferreira and D. F. M. Torres, Generalized retarded integral inequalities, Appl. Math. Lett. 22 (2009), no. 6, 876-881.

6. R. A. C. Ferreira and D. F. M. Torres, Some linear and nonlinear integral inequalities on time scales in two independent variables, Nonlinear Dyn. Syst. Theory 9 (2009), no. 2, 161-169.

7. R. A. C. Ferreira, Constantin integral inequalities on time scales, Arch. Math. (Basel) 93 (2009), no. 2, 153-163.

8. R. A. C. Ferreira, Existence of solutions to some retarded integrodifferential equations via the topological transversality theorem, Nonlinear Anal. 72 (2010), no. 6, 3062-3068.

9. R. A. C. Ferreira, Existence of solution to an integrodynamic equation, Dynam. Systems Appl. 19 (2010), 289-301.

10. M. Bohner, R. A. C. Ferreira and D. F. M. Torres, Integral inequalities and their applications to the calculus of variations on time scales, Math. Inequal. Appl. 13 (2010), no. 3, 511-522.

11. R. A. C. Ferreira, Nontrivial solutions for fractional q-difference boundary value problems, Electron. J. Qual. Theory Differ. Equ. 2010, No. 70, 10 pp.

12. N. R. O. Bastos, R. A. C. Ferreira and D. F. M. Torres, Necessary optimality conditions for fractional difference problems of the calculus of variations, Discrete Contin. Dyn. Syst. 29 (2011), no. 2, 417-437.

13. R. A. C. Ferreira, A. B. Malinowska and D. F. M. Torres, Optimality conditions for the calculus of variations with higher-order delta derivatives, Appl. Math. Lett. 24 (2011), no. 1, 87-92.

14. N. R. O. Bastos, R. A. C. Ferreira and D. F. M. Torres, Discrete-time fractional variational problems, Signal Processing 91 (2011), 513-524.

15. R. A. C. Ferreira, Positive solutions for a class of boundary value problems with fractional q-differences, Comput. Math. Appl. 61 (2011), no. 2, 367-373.

16. R. A. C. Ferreira and D. F. M. Torres, Fractional h-difference equations arising from the calculus of variations, Appl. Anal. Discrete Math. 5 (2011), no. 1, 110-121.

17. M. Bohner and R. A. C. Ferreira, Some discrete fractional inequalities of Chebyshev type, Afr Diaspora J. Math. 11 (2011), no. 2, 132-137.

18. R. Almeida, R. A. C. Ferreira and D. F. M. Torres, Isoperimetric problems of the calculus of variations with fractional derivatives, Acta Math. Sci. Ser. B Engl. Ed. 32 (2012), no. 2, 619-630.

19. R. A. C. Ferreira, A discrete fractional Gronwall inequality, Proc. Amer. Math. Soc. 140 (2012), no. 5, 1605-1612.

20. R. A. C. Ferreira, Nonnegative Solutions of a Fredholm Type Integral Equation with Applications to Boundary Value Problems, Acta Appl. Math. 121 (2012), 45-56.

21. R. A. C. Ferreira, A uniqueness result for a fractional differential equation, Fract. Calc. Appl. Anal. 15 (2012), no. 4, 611-615.

22. R. A. C. Ferreira and C. S. Goodrich, Positive solution for a discrete fractional periodic boundary value problem, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 19 (2012), no. 5, 545-557.

23. R. A. C. Ferreira, Existence and uniqueness of solution to some discrete fractional boundary value problems of order less than one, J. Difference Equ. Appl. 19 (2013), no. 5, 712-718.

24. R. A. C. Ferreira, A probability problem arising from the security of the temporal key hash of WPA, Wireless Pers. Commun. 70 (2013), no. 4, 1235-1241.

25. R. A. C. Ferreira, A Lyapunov-type inequality for a fractional boundary value problem, Fract. Calc. Appl. Anal. 16 (2013), no. 4, 978-984.

26. R. A. C. Ferreira, A Nagumo-type uniqueness result for an nth order differential equation, Bull. London Math. Soc. 45 (2013), no. 5, 930-934.

27. R. A. C. Ferreira, On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function, J. Math. Anal. Appl. 412 (2014), no. 2, 1058-1063.

28. R. A. C. Ferreira, Positive solutions of a nonlinear q-fractional difference equation with integral boundary conditions, Int. J. Difference Equ. 9 (2014), no. 2, 135-145.

29. P. R. S. Antunes and R. A. C. Ferreira, An augmented-RBF method for solving fractional Sturm-Liouville eigenvalue problems, SIAM J. Sci. Comput. 37 (2015), no. 1, A515-A535.

30. R. A. C. Ferreira and C. S. Goodrich, On positive solutions to fractional difference inclusions, Analysis (Berlin) 35 (2015), no. 2, 73-83.

31. R. A. C. Ferreira and A. B. Malinowska, A counterexample to a Frederico-Torres fractional Noether-type theorem, J. Math. Anal. Appl. 429 (2015), no. 2, 1370-1373.

32. R. A. C. Ferreira, Some Discrete Fractional Lyapunov-type inequalities, Fract. Differ. Calc. 5 (2015), no. 1, 87-92.

33. R. A. C. Ferreira, Existence and uniqueness of solutions for two-point fractional boundary value problems, Electron. J. Differential Equations (2016), Paper No. 202, 5 pp.

34. R. A. C. Ferreira, Lyapunov-Type inequalities for some sequential fractional boundary value problems, Adv. Dyn. Syst. Appl. 11 (2016), no. 1, 33-43.

35. R. A. C. Ferreira, Lyapunov-type inequality for an anti-periodic fractional boundary value problem, Fract. Calc. Appl. Anal. 20 (2017), no. 1, 284-291.

36. P. R. S. Antunes and R. A. C. Ferreira, Analysis of a class of boundary value problems depending on left and right Caputo fractional derivatives, Commun. Nonlinear Sci. Numer. Simul. 48 (2017), 398-413.

37. R. A. C. Ferreira, A new look at Bernoulli's inequality, Proc. Amer. Math. Soc. 146 (2018), no. 3, 1123-1129.

38. R. A. C. Ferreira, A de La Vallée Poussin type inequality on time scales, Results Math. 73 (2018), no. 3, Art. 88, 9 pp.  

39. R. A. C. Ferreira and C. M. Silva, A nonautonomous epidemic model on time scales, J. Difference Equ. Appl. 24 (2018), no. 8, 1295-1317.

40. R. A. C. Ferreira, Addendum to "Some Discrete Fractional Lyapunov-type inequalities'' [Fract. Differ. Calc. 5 (2015), no. 1, 87-92], Fract. Differ. Calc. 8 (2018), no. 2, 357-359.

41. R. A. C. Ferreira, Note on a uniqueness result for a two-point fractional boundary value problem, Appl. Math. Lett. 90 (2019), 75-78.

42. R. A. C. Ferreira, Novel Lyapunov-type inequalities for sequential fractional boundary value problems, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), no. 1, 171-179. 

43. R. A. C. Ferreira, Anti-symmetry of the second eigenfunction of the fractional Laplace operator in a 3-D ball, NoDEA Nonlinear Differential Equations Appl. 26 (2019), no. 1, 26:6.

44. R. A. C. Ferreira, Corrigendum to "Nontrivial solutions for fractional q-difference boundary value problems'' [Electron. J. Qual. Theory Differ. Equ. 2010, No. 70, 1--10], Electron. J. Qual. Theory Differ. Equ. 2019, No. 44, 2 pp.

45. R. A. C. Ferreira, Fractional de la Vallée Poussin inequalities, Math. Inequal. Appl. 22 (2019), no. 3, 917-930.

46. R. A. C. Ferreira and J. Tenreiro Machado, An entropy formulation based on the generalized Liouville fractional derivative, Entropy 21 (2019), no. 7, Paper No. 638, 9 pp. 

47. R. A. C. Ferreira, Fractional calculus of variations: a novel way to look at it, Fract. Calc. Appl. Anal. 22 (2019), no. 4, 1133-1144.

48. R. A. C. Ferreira, An entropy based on a fractional difference operator, J. Difference Equ. Appl.  27 (2021), no. 2, 218-222.

49. H. Alzer and R. A. C. Ferreira, Concavity and generalized entropy, Appl. Math. E-Notes 21 (2021), 37-43.

50. R. A. C. Ferreira, Discrete weighted fractional calculus and applications, Nonlinear Dynamics, 104 (2021), 2531-2536.

51. R. A. C. Ferreira, Generalized discrete operators, Journal of Fractional Calculus and Nonlinear Systems, (2021) 2 (1): 18-23.

52. L. Bourdin and R. A. C. Ferreira, Legendre's Necessary Condition for Fractional Bolza Functionals with Mixed Initial/Final Constraints, J. Optim. Theory Appl. 190 (2021), no. 2, 672-708. 

53. R. A. C. Ferreira, Two-point fractional boundary value problems, J. Integral Equations Appl. 33 (2021), no. 2, 229-236.

54. R. A. C. Ferreira, Discrete fractional calculus and the Saalschutz theorem, Bull. Sci. Math. 174 (2022), Paper No. 103086. 

55. R. A. C. Ferreira, Stability of a class of entropies based on fractional calculus, J. Appl. Anal. 28 (2022), no. 1, 105-107. 

56. R. A. C. Ferreira, Addendum to "A new look at Bernoulli's inequality", Proc. Amer. Math. Soc. 151 (2023), no. 1, 85-86.

57. R. A. C. Ferreira and T. Simon, Convolution of beta prime distribution, Trans. Amer. Math. Soc. 376 (2023), no.  2, 855-890. 

58. R. A. C. Ferreira, Sign of the solutions of linear fractional differential equations and Some applications, Vietnam J. Math. 51 (2023), no. 2, 451-461.

59. T. Cuchta and R. A. C. Ferreira, The heat equation on time scales, Opuscula Math. 43 (2023), no. 4, 475-491.

60. R. A. C. Ferreira, Hartman-Wintner inequality for a Caputo fractional boundary value problem, Rocky Mountain J. Math. 54 (2024), no. 1, 137-141.

61. R. A. C. Ferreira, Calculus of variations with higher order Caputo fractional derivatives. Arab. J. Math. 13 (2024), 91--101.

62. R. A. C. Ferreira and C. D. A. Rocha, Discrete convolution operators and equations, Fract. Calc. Appl. Anal. 27 (2024), no. 2, 757-771.

Chapters in books

1. R. A. C. Ferreira and D. F. M. Torres, Higher-order calculus of variations on time scales, in Mathematical control theory and finance, 149-159, Springer, Berlin, 2008.

2. R. A. C. Ferreira and D. F. M. Torres. Retarded integral inequalities of Gronwall-Bihari type, Inequality Theory and Applications, 61-69, Nova Science Publishers, Volume 6, 2010.

3. R. A. C. Ferreira and D. F. M. Torres, Isoperimetric problems of the calculus of variations on time scales. Nonlinear Analysis and Optimization II. Optimization, Vol. 514, pp. 123-131, Contemp. Math., Amer. Math. Soc., Providence, RI, 2010.

4. R. A. C. Ferreira, Lyapunov inequalities for some differential equations with integral type boundary conditions,  Advances in Mathematical Inequalities and Applications, Springer International Publishing (2018), 59-70.