Institute of Mathematics

References:
[1] D. D. Ang, K. Schmitt, L. K. Vy: A multidimensional analogue of the Denjoy-Perron-Henstock-Kurzweil integral. Bull. Belg. Math. Soc. - Simon Stevin 4 (1997), 355-371. DOI 10.36045/bbms/1105733252 | MR 1457075 | Zbl 0929.26009
[2] A. Atangana: Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties. Physica A 505 (2018), 688-706. DOI 10.1016/j.physa.2018.03.056 | MR 3807252 | Zbl 07550314
[3] A. Atangana, J. F. Gómez-Aguilar: Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena. Eur. Phys. J. Plus 133 (2018), Article ID 133, 22 pages. DOI 10.1140/epjp/i2018-12021-3
[4] A. Atangana, J. F. Gómez-Aguilar: Numerical approximation of Riemann-Liouville definition of fractional derivative: From Riemann-Liouville to Atangana-Baleanu. Numer. Methods Partial Differ. Equations 34 (2018), 1502-1523. DOI 10.1002/num.22195 | MR 3843531 | Zbl 1417.65113
[5] A. Atangana, S. Qureshi: Modeling attractors of chaotic dynamical systems with fractal-fractional operators. Chaos Solitons Fractals 123 (2019), 320-337. DOI 10.1016/j.chaos.2019.04.020 | MR 3941450 | Zbl 1448.65268
[6] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo: Fractional Calculus: Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos 3. World Scientific, Hackensack (2012). DOI 10.1142/10044 | MR 2894576 | Zbl 1248.26011
[7] J. H. Barrett: Differential equations of non-integer order. Can. J. Math. 6 (1954), 529-541. DOI 10.4153/CJM-1954-058-2 | MR 0064936 | Zbl 0058.10702
[8] B. Bongiorno: Relatively weakly compact sets in the Denjoy space. J. Math. Study 27 (1994), 37-44. MR 1318256 | Zbl 1045.26502
[9] B. Bongiorno, T. V. Panchapagesan: On the Alexiewicz topology of the Denjoy space. Real Anal. Exch. 21 (1995/96), 604-614. MR 1407272 | Zbl 0879.26028
[10] E. M. Bonotto, M. Federson, P. Muldowney: A Feynman-Kac solution to a random impulsive equation of Schrödinger type. Real Anal. Exch. 36 (2010/11), 107-148. DOI 10.14321/realanalexch.36.1.0107 | MR 3016407 | Zbl 1246.28008
[11] N. L. Carothers: Real Analysis. Cambridge University Press, Cambridge (2000). DOI 10.1017/CBO9780511814228 | MR 1772332 | Zbl 0997.26003
[12] T. S. Chew, F. Flordeliza: On $x'=f(t,x)$ and Henstock-Kurzweil integrals. Differ. Integral Equ. 4 (1991), 861-868. DOI 10.57262/die/1371225020 | MR 1108065 | Zbl 0733.34004
[13] P. C. Das, R. R. Sharma: On optimal controls for measure delay-differential equations. SIAM. J. Control 9 (1971), 43-61. DOI 10.1137/0309005 | MR 0274898 | Zbl 0283.49003
[14] P. C. Das, R. R. Sharma: Existence and stability of measure differential equations. Czech. Math. J. 22 (1972), 145-158. DOI 10.21136/CMJ.1972.101082 | MR 0304815 | Zbl 0241.34070
[15] K. Diethelm: The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Lecture Notes in Mathematics 2004. Springer, Berlin (2010). DOI 10.1007/978-3-642-14574-2 | MR 2680847 | Zbl 1215.34001
[16] K. Diethelm, A. D. Freed: On the solution of nonlinear fractional-order differential equations used in the modeling of viscoplasticity. Scientific Computing in Chemical Engineering II. Springer, Berlin (1999). DOI 10.1007/978-3-642-60185-9_24
[17] J. J. Duistermaat, J. A. C. Kolk: Distributions: Theory and Applications. Cornerstones. Birkhäuser, Boston (2010). DOI 10.1007/978-0-8176-4675-2 | MR 2680692 | Zbl 1213.46001
[18] J. F. Gómez-Aguilar, A. Atangana: New insight in fractional differentiation: Power, exponential decay and Mittag-Leffler laws and applications. Eur. Phys. J. Plus 132 (2017), Article ID 13, 21 pages. DOI 10.1140/epjp/i2017-11293-3
[19] R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics 4. AMS, Providence (1994). DOI 10.1090/gsm/004 | MR 1288751 | Zbl 0807.26004
[20] N. Hayek, J. Trujillo, M. Rivero, B. Bonilla, J. C. Moreno: An extension of Picard-Lindelöff theorem to fractional differential equations. Appl. Anal. 70 (1999), 347-361. DOI 10.1080/00036819808840696 | MR 1688864 | Zbl 1030.34003
[21] R. Hilfer (ed.): Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000). DOI 10.1142/3779 | Zbl 0998.26002
[22] L. Hörmander: The Analysis of Linear Partial Differential Operators I. Distribution Theory and Fourier Analysis. Grundlehren der Mathematischen Wissenschaften 256. Springer, Berlin (1990). DOI 10.1007/978-3-642-96750-4 | MR 1996773 | Zbl 0712.35001
[23] A. A. Kilbas, B. Bonilla, J. J. Trujillo: Existence and uniqueness theorems for nonlinear fractional differential equations. Demonstr. Math. 33 (2000), 583-602. DOI 10.1515/dema-2000-0315 | MR 1791723 | Zbl 0964.34004
[24] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies 204. Elsevier, Amsterdam (2006). DOI 10.1016/s0304-0208(06)x8001-5 | MR 2218073 | Zbl 1092.45003
[25] P. Krejčí, H. Lamba, G. A. Monteiro, D. Rachinskii: The Kurzweil integral in financial market modeling. Math. Bohem. 141 (2016), 261-286. DOI 10.21136/MB.2016.18 | MR 3499787 | Zbl 1389.34140
[26] F. Mainardi: Fractional calculus: Some basic problems in continuum and statistical mechanics. Fractals and Fractional Calculus in Continuum Mechanics. CISM Courses and Lectures 378. Springer, Vienna (1997), 291-348. DOI 10.1007/978-3-7091-2664-6_7 | MR 1611587
[27] K. S. Miller, B. Ross: An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley & Sons, New York (1993). MR 1219954 | Zbl 0789.26002
[28] G. A. Monteiro, B. Satco: Distributional, differential and integral problems: Equivalence and existence results. Electron. J. Qual. Theory Differ. Equ. 2017 (2017), Article ID 7, 26 pages. DOI 10.14232/ejqtde.2017.1.7 | MR 3606985 | Zbl 1413.34062
[29] G. A. Monteiro, A. Slavík, M. Tvrdý: Kurzweil-Stieltjes Integral: Theory and Applications. Series in Real Analysis 15. World Scientific, Singapore (2019). DOI 10.1142/9432 | MR 3839599 | Zbl 1437.28001
[30] M. G. Morales, Z. Došlá: Weighted Cauchy problem: Fractional versus integer order. J. Integral Equations Appl. 33 (2021), 497-509. DOI 10.1216/jie.2021.33.497 | MR 4393381 | Zbl 1510.34021
[31] M. G. Morales, Z. Došlá, F. J. Mendoza: Riemann-Liouville derivative over the space of integrable distributions. Electron Res. Arch. 28 (2020), 567-587. DOI 10.3934/era.2020030 | MR 4097636 | Zbl 07220320
[32] T. Morita, K. Sato: Solution of fractional differential equation in terms of distribution theory. Interdiscip. Inf. Sci. 12 (2006), 71-83. DOI 10.4036/iis.2006.71 | MR 2267319 | Zbl 1121.34003
[33] P. Muldowney: Feynman's path integrals and Henstock's non-absolute integration. J. Appl. Anal. 6 (2000), 1-24. DOI 10.1515/JAA.2000.1 | MR 1758185 | Zbl 0963.28012
[34] A. V. Pskhu: Initial-value problem for a linear ordinary differential equation of noninteger order. Sb. Math. 202 (2011), 571-582. DOI 10.1070/SM2011v202n04ABEH004156 | MR 2830238 | Zbl 1226.34005
[35] J. Sabatier, O. P. Agrawal, J. A. T. Machado (eds.): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007). DOI 10.1007/978-1-4020-6042-7 | MR 2432163 | Zbl 1116.00014
[36] A. H. H. Salem, M. Cichoń: On solutions of fractional order boundary value problems with integral boundary conditions in Banach spaces. J. Funct. Spaces Appl. 2013 (2013), Article ID 428094, 13 pages. DOI 10.1155/2013/428094 | MR 3071357 | Zbl 1272.34010
[37] S. G. Samko, A. A. Kilbas, O. I. Marichev: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, New York (1993). MR 1347689 | Zbl 0818.26003
[38] W. W. Schmaedeke: Optimal control theory for nonlinear vector differential equations containing measures. J. SIAM Control, Ser. A 3 (1965), 231-280. DOI 10.1137/0303019 | MR 0189870 | Zbl 0161.29203
[39] Š. Schwabik: Generalized Ordinary Differential Equations. Series in Real Analysis 5. World Scientific, Singapore (1992). DOI 10.1142/1875 | MR 1200241 | Zbl 0781.34003
[40] D. R. Smart: Fixed Point Theorems. Cambridge Tracts in Mathematics 66. Cambridge University Press, Cambridge (1980). MR 0467717 | Zbl 0427.47036
[41] E. Talvila: The distributional Denjoy integral. Real Anal. Exch. 33 (2007/08), 51-82. DOI 10.14321/realanalexch.33.1.0051 | MR 2402863 | Zbl 1154.26011
[42] E. Talvila: Convolutions with the continuous primitive integral. Abstr. Appl. Anal. 2009 (2009), Article ID 307404, 18 pages. DOI 10.1155/2009/307404 | MR 2559282 | Zbl 1192.46039
[43] Y. T. Xu: Functional Differential Equations and Measure Differential Equations. Zhongshan University Press, Guangzhou (1988). (In Chinese.)
[44] G. Ye, W. Liu: The distributional Henstock-Kurzweil integral and applications. Monatsh. Math. 181 (2016), 975-989. DOI 10.1007/s00605-015-0853-1 | MR 3563309 | Zbl 1362.45009
[45] G. Ye, W. Liu: The distributional Henstock-Kurzweil integral and applications: A survey. J. Math. Study 49 (2016), 433-448. DOI 10.4208/jms.v49n4.16.06 | MR 3592995 | Zbl 1374.26021
[46] G. Ye, M. Zhang, E. Liu, D. Zhao: Existence and uniqueness of solutions to distributional differential equations involving Henstock-Kurzweil-Stieltjes integrals. Rev. Unión Mat. Argent. 60 (2019), 443-458. DOI 10.33044/revuma.v60n2a11 | MR 4049796 | Zbl 1432.34005
[47] H. Zhou, G. Ye, W. Liu, O. Wang: The distributional Henstock-Kurzweil integral and measure differential equations. Bull. Iran. Math. Soc. 41 (2015), 363-374. MR 3345524 | Zbl 1373.26008