Publications

The following are my research papers which have been published or accepted for publication.

88.  A. Fernandez, H.M. Fahad, A historical survey of fractional calculus with respect to functions (ψ-fractional calculus), in: J. Virtanen (ed.), Proceedings of the International Workshop on Operator Theory and its Applications 2023, Springer/Birkhäuser, accepted 2024.

87.  I.A. Saleh, A. Fernandez, On the possibility of Mikusiński's operational calculus for the fractional Laplacian, Jordan Journal of Mathematics and Statistics, accepted 2024.

86.  W. Yasin, A. Fernandez, Fractional powers of Clifford d-bar and radial derivatives, Journal of Mathematical Analysis and Applications 542(2) (2025), 128952.

85.  W. Yasin, A. Fernandez, Fractional polyanalyticity, in: M. Ferreira, N. Faustino, U. Kähler, N. Vieira, Hypercomplex Analysis and Its Applications, Springer/Birkhäuser, Cham, accepted 2024.

84.  A. Fernandez, Multi-dimensional operators with Sonine kernels, in: A.H. Hasanoğlu, R. Novikov, K. van Bockstal (eds.), Extended Abstracts IPMS 2024 Conference: Inverse Problems: Modeling and Simulation, Springer, accepted 2024.

83.  N. Rani, A. Fernandez, Mikusiński's operational calculus for multi-dimensional fractional operators with applications to fractional PDEs, Communications in Nonlinear Science and Numerical Simulation 138 (2024), 108249.

82.  A. Fernandez, H.M. Fahad, General transmutation relations and their applications, in: S. Victor (ed.), 12th IFAC Conference on Fractional Differentiation and its Applications ICFDA 2024, IFAC-PapersOnLine, 58(12) (2024), pp. 149–154.

81.  A. Fernandez, N. Rani, Mikusiński’s operational calculus for fractional operators with different kernels, in: S. Victor (ed.), 12th IFAC Conference on Fractional Differentiation and its Applications ICFDA 2024, IFAC-PapersOnLine, 58(12) (2024), pp. 220–225.

80.  A. Fernandez, J.E. Restrepo, J.-D. Djida, On the fractional Laplacian of a function with respect to another function, Mathematical Methods in the Applied Sciences 47(18) (2024), pp. 14079–14110.

79.  A. Fernandez, On complex orders in fractional calculus: floors, ceilings, and analytic continuation, in: S. Victor (ed.), 12th IFAC Conference on Fractional Differentiation and its Applications ICFDA 2024, IFAC-PapersOnLine, 58(12) (2024), pp. 143–148.

78.  A. Fernandez, Abstract algebraic construction in fractional calculus: parametrised families with semigroup properties, Complex Analysis and Operator Theory 18 (2024), 50.

77.  A. Fernandez, M. Saadetoğlu, Algebraic results on rngs of singular functions, Forum Mathematicum 36(6) (2024), pp. 1645–1657.

76.  B. Gürbüz, A. Fernandez, Editorial for Special Issue “Numerical and Analytical Methods for Differential Equations and Systems”, Fractal and Fractional 8(1) (2024), 59.

75.  A. Fernandez, S.C. Buranay, The Peano–Sard theorem for Caputo fractional derivatives, Journal of Computational and Applied Mathematics 441 (2024), 115705.

74.  M. Al-Refai, A. Fernandez, Comparison principles for a class of general integro-differential inequalities with applications, Computational and Applied Mathematics, 43 (2024), 99.

73.  A. Fernandez, C. Güder, W. Yasin, Fractional powers of the quaternionic d-bar derivative, Advances in Applied Clifford Algebras 34 (2024), 2.

72.  S.S. Isah, A. Fernandez, M.A. Özarslan, On univariate fractional calculus with general bivariate analytic kernels, Computational and Applied Mathematics 42 (2023), 228.

71.  A. Fernandez, C. Güder, W. Yasin, On fractional quaternionic d-bar derivatives, in: M. Ruzhansky, B. Torebek (eds.), Extended Abstracts MWCAPDE 2023: Methusalem Workshop on Classical Analysis and Partial Differential Equations, Springer, accepted 2023.

70.  S.S. Isah, A. Fernandez, M.A. Özarslan, On bivariate fractional calculus with general univariate analytic kernels, Chaos, Solitons and Fractals 171 (2023), 113495.

69.  A. Fernandez, N. Rani, Ž. Tomovski, An operational calculus approach to Hilfer–Prabhakar fractional derivatives, Banach Journal of Mathematical Analysis 17 (2023), 33.

68.  A. Fernandez, M. Al-Refai, A rigorous analysis of integro-differential operators with non-singular kernels, Fractal and Fractional 7(3) (2023), 213.

67.  M. Al-Refai, A. Fernandez, Generalising the fractional calculus with Sonine kernels via conjugations, Journal of Computational and Applied Mathematics 427C (2023), 115159.

66.  A. Fernandez, Mikusiński’s operational calculus for general conjugated fractional derivatives, Boletín de la Sociedad Matemática Mexicana 29(1) (2023), 25.

65.  S. Emin, A. Fernandez, Incommensurate multi-term fractional differential equations with variable coefficients with respect to functions, Mathematical Methods in the Applied Sciences 46(8) (2023), pp. 8618–8631.

64.  C. Kürt, A. Fernandez, M.A. Özarslan, Two unified families of bivariate Mittag-Leffler functions, Applied Mathematics and Computation 443 (2023), 127785.

63.  A. Fernandez, J.E. Restrepo, D. Suragan, A new representation for the solutions of fractional differential equations with variable coefficients, Mediterranean Journal of Mathematics 20 (2023), 27.

62.  N. Rani, A. Fernandez, An operational calculus formulation of fractional calculus with general analytic kernels, Electronic Research Archive 30(12) (2022), pp. 4238–4255.

61.  K.D. Kucche, A.D. Mali, A. Fernandez, H.M. Fahad, On tempered Hilfer fractional derivatives with respect to functions and the associated fractional differential equations, Chaos, Solitons and Fractals 163 (2022), 112547.

60.  A. Fernandez, J.E. Restrepo, D. Suragan, On linear fractional differential equations with variable coefficients, Applied Mathematics and Computation 432 (2022), 127370.

59.  A. Fernandez, H.M. Fahad, On the importance of conjugation relations in fractional calculus, Computational and Applied Mathematics 41 (2022), 246.

58.  A.D. Mali, K. Kucche, A. Fernandez, H.M. Fahad, On tempered fractional calculus with respect to functions and the associated fractional differential equations, Mathematical Methods in the Applied Sciences 45(17) (2022), pp. 11134–11157.

57.  A. Fernandez, J.E. Restrepo, D. Suragan, Prabhakar-type linear differential equations with variable coefficients, Differential and Integral Equations 35 (2022), pp. 581–610.

56.  P.O. Mohammed, A. Fernandez, Integral inequalities in fractional calculus with general analytic kernels, Filomat 37(11) (2023) pp. 3659–3669.

55.  A. Fernandez, H.M. Fahad, Weighted fractional calculus: a general class of operators, Fractal and Fractional 6 (2022), 208.

54.  N. Rani, A. Fernandez, Mikusinski’s operational calculus for Prabhakar fractional calculus, Integral Transforms and Special Functions 33(12) (2022), pp. 945–965.

53.  N. Rani, A. Fernandez, Solving Prabhakar differential equations using Mikusinski’s operational calculus, Computational and Applied Mathematics 41 (2022), 107.

52.  A. Fernandez, M.A. Özarslan, C. Kürt, A catalogue of semigroup properties for integral operators with Fox–Wright kernel functions, Studies in Applied Mathematics 148 (2022), pp. 1477–1518.

51.  M.A. Özarslan, A. Fernandez, I. Area, Editorial for Special Issue “Fractional Calculus and Special Functions with Applications”, Fractal and Fractional 5(4) (2021), 224. 

50.  A. Fernandez, Mikusiński’s Operational Calculus applied in General Classes of Fractional Calculus, in: A. Dzielinski, D. Sierociuk, P. Ostalczyk (eds.), Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA'21), Springer, Cham, 2022.

49.  A. Fernandez, J.E. Restrepo, D. Suragan, Linear differential equations with variable coefficients and Mittag-Leffler kernels, Alexandria Engineering Journal 61 (2022), pp. 4757–4763.

48.  A. Fernandez, J.E. Restrepo, D. Suragan, Lipschitz and Fourier type conditions with moduli of continuity in rank 1 symmetric spaces, Monatshefte für Mathematik 197 (2022), pp. 353–364.

47.  C.M.S. Oumarou, H.M. Fahad, J.-D. Djida, A. Fernandez, On fractional calculus with analytic kernels with respect to functions, Computational and Applied Mathematics 40 (2021), 244.

46.  A. Fernandez, J.-D. Djida, Fractional differential relations for the Lerch zeta function, Archiv der Mathematik 117 (2021), pp. 515–527.

45.  H.M. Fahad, M. u. Rehman, A. Fernandez, On Laplace transforms with respect to functions and their applications to fractional differential equations, Mathematical Methods in the Applied Sciences 46(7) (2023), pp. 8304–8323.

44.  A. Fernandez, S. Ali, A. Zada, On non-instantaneous impulsive fractional differential equations and their equivalent integral equations, Mathematical Methods in the Applied Sciences 44 (2022), pp. 13979–13988.

43.  R. Nigmatullin, D. Baleanu, A. Fernandez, Balance equations with generalised memory and the emerging fractional kernels, Nonlinear Dynamics 104(4) (2021), pp. 4149–4161.

42.  H.M. Fahad, A. Fernandez, Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations, Applied Mathematics and Computation 409 (2021), 126400.

41.  M.A. Özarslan, A. Fernandez, On a five-parameter Mittag-Leffler function and thecorresponding bivariate fractional operators, Fractal and Fractional 5(2) (2021), 45. 

40.  R. Daher, A. Fernandez, J.E. Restrepo, Characterising extended Lipschitz type conditions with moduli of continuity, Results in Mathematics 76 (2021), 125.

39.  A. Fernandez, S. Uçar, N. Özdemir, Solving a well-posed fractional initial value problem by a complex approach, Fixed Point Theory and Algorithms for Sciences and Engineering 2021 (2021), 11.

38.  A. Fernandez, C. Ustaoğlu, M.A. Özarslan, On the analytical development of incomplete Riemann–Liouville fractional calculus, Turkish Journal of Mathematics 45(3) (2021), pp. 1418–1443.

37.  M.A. Özarslan, A. Fernandez, On the fractional calculus of multivariate Mittag-Leffler functions, International Journal of Computer Mathematics 99(2) (2022), pp. 247–273.

36.  H.M. Fahad, A. Fernandez, Operational calculus for Riemann-Liouville fractional calculus with respect to functions and the associated fractional differential equations, Fractional Calculus and Applied Analysis 24(2) (2021), pp. 518–540.

35.  A. Fernandez, D. Baleanu, Classes of Operators in Fractional Calculus: a Case Study, Mathematical Methods in the Applied Sciences 44(11) (2021), pp. 9143–9162.

34.  A. Ahmadova, I.T. Huseynov, A. Fernandez, N.I. Mahmudov, Trivariate Mittag-Leffler functions used to solve multi-order systems of fractional differential equations, Communications in Nonlinear Science and Numerical Simulation 97C (2021), 105735.

33.  H.M. Fahad, A. Fernandez, M. u. Rehman, M. Siddiqi, Tempered and Hadamard-type fractional calculus with respect to functions, Mediterranean Journal of Mathematics 18 (2021), 143.

32.  A. Fernandez, I. Husain, Modified Mittag-Leffler functions with applications in complex formulae for fractional calculus, Fractal and Fractional 4(3) (2020), 45.

31.  I.T. Huseynov, A. Ahmadova, A. Fernandez, N.I. Mahmudov, Explicit analytic solutions of incommensurate fractional differential equation systems, Applied Mathematics and Computation 390C (2021), 125590.

30.  A. Fernandez, C. Kürt, M.A. Özarslan, A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators, Computational and Applied Mathematics 39 (2020), 200.

29.  A. Fernandez, T. Abdeljawad, D. Baleanu, Relations between fractional models with three-parameter Mittag-Leffler kernels, Advances in Difference Equations, 2020 (2020), 186.

28.  D. Baleanu, A. Fernandez, A. Akgül, On a fractional operator combining proportional and classical differintegrals, Mathematics 8(3) (2020), 360.

27.  C. Kürt, M.A. Özarslan, A. Fernandez, On a certain bivariate Mittag-Leffler function analysed from a fractional-calculus point of view, Mathematical Methods in the Applied Sciences 44 (2021), pp. 2600–2620.

26.  A. Fernandez, C. Bouzouina, Fractionalisation of complex d-bar derivatives, Complex Variables and Elliptic Equations 66(3) (2021), pp. 437–475.

25.  A. Fernandez, P.O. Mohammed, Hermite–Hadamard inequalities in fractional calculus defined using Mittag-Leffler kernels, Mathematical Methods in the Applied Sciences 44(10) (2021), pp. 8414–8431.

24.  D. Baleanu, A. Fernandez, On fractional operators and their classifications, Mathematics 7(9) (2019), 830.

23.  J.-D. Djida, A. Fernandez, I. Area, Well-posedness results for fractional semi-linear wave equations, Discrete & Continuous Dynamical Systems – B 25(2) (2020), pp. 569–597.

22.  T. Abdeljawad, A. Fernandez, On a new class of fractional difference-sum operators with discrete Mittag-Leffler kernels, Mathematics 7(9) (2019), 772.

21.  A. Fernandez, C. Ustaoğlu, On some analytic properties of tempered fractional calculus, Journal of Computational and Applied Mathematics 366 (2020), 112400.

20.  A. Fernandez, D. Baleanu, H.M. Srivastava, Corrigendum to “Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions" [Commun. Nonlinear Sci. Numer. Simulat. 67 (2019) 517–527, Communications in Nonlinear Science and Numerical Simulation 82 (2020), 104963.

19.  A.K. Golmankhaneh, S. Ashrafi, D. Baleanu, A. Fernandez, Brownian motion on Cantor sets, International Journal of Nonlinear Science and Numerical Simulation, 21 (2020), pp. 275–281.

18.  A.K. Golmankhaneh, A. Fernandez, Random variables and stable distributions on fractal Cantor sets, Fractal and Fractional 3(2) (2019), 31.

17.  H.M. Srivastava, A. Fernandez, D. Baleanu, Some new fractional-calculus connections between Mittag-Leffler functions, Mathematics 7(6) (2019), 485.

16.  A. Fernandez, A complex analysis approach to Atangana–Baleanu fractional calculus, Mathematical Methods in the Applied Sciences 44(10) (2021), pp. 8070–8087.

15.  A. Fernandez, M.A. Özarslan, D. Baleanu, On fractional calculus with general analytic kernels, Applied Mathematics and Computation 354 (2019), pp. 248–265.

14.  A. Fernandez, D. Baleanu, On a new definition of fractional differintegrals with Mittag-Leffler kernel, Filomat 33(1) (2019), pp. 245–254.

13.  A.K. Golmankhaneh, A. Fernandez, Fractal calculus of functions on Cantor tartan spaces, Fractal and Fractional 2(4) (2018).

12.  A. Fernandez, D. Baleanu, Differintegration with respect to functions in fractional models involving Mittag-Leffler functions, SSRN 3275746 (2018).

11.  J.-D. Djida, A. Fernandez, Interior regularity estimates for a degenerate elliptic equation with mixed boundary conditions, Axioms 7(3) (2018), pp. 1–16.

10.  A. Fernandez, D. Baleanu, A.S. Fokas, Solving PDEs of fractional order using the unified transform method, Applied Mathematics and Computation 339C (2018), pp. 738–749.

9.  A. Fernandez, D. Baleanu, H.M. Srivastava, Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions, Communications in Nonlinear Science and Numerical Simulation, 67 (2019), pp. 517–527.

8.  A.K. Golmankhaneh, A. Fernandez, A.K. Golmankhaneh, D. Baleanu, Diffusion on middle-ξ Cantor sets, Entropy 20(7) (2018).

7.  A. Fernandez, A.S. Fokas, Asymptotics to all orders of the Hurwitz zeta function, Journal of Mathematical Analysis and Applications 465(1) (2018), pp. 423–458.

6.  A. Fernandez, The Lerch zeta function as a fractional derivative, Banach Center Publications 118 (2019), pp. 113–124. Preprint available from arXiv:1804.07936.

5.  A. Fernandez, An elliptic regularity theorem for fractional partial differential operators, Computational and Applied Mathematics 37 (2018), pp. 5542–5553.

4.  A. Fernandez, D. Baleanu, The mean value theorem and Taylor's theorem for fractional derivatives with Mittag-Leffler kernel, Advances in Difference Equations 2018:86 (2018).

3.  A. Fernandez, E.A. Spence, A.S. Fokas, Uniform asymptotics as a stationary point approaches an endpoint, IMA Journal of Applied Mathematics 83(1) (2018), pp. 204–242. 

2.  D. Baleanu, A. Fernandez, On some new properties of fractional derivatives with Mittag-Leffler kernel, Communications in Nonlinear Science and Numerical Simulation 59 (2018), pp. 444–462.

1.  D. Baleanu, A. Fernandez, A generalisation of the Malgrange–Ehrenpreis theorem to find fundamental solutions to fractional PDEs, Electronic Journal of Qualitative Theory of Differential Equations 15 (2017), pp. 1–12.