Cauchy integral on time scales: constructive sense
Resumo
We study the Cauchy Delta (resp. Nabla) Integral and the Cauchy α-Integral on time scales in a constructive sense, and state and proof the Cauchy Criteria of Integrability using these definitions and also establish a few results
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Referências
Ravi P. Agarwal and Martin Bohner, Basic Calculus on Time Scales and some of its Applications, Results in Mathematics, 35, (1999), pp. 3-22.
F.Merdivenci Atici , G.Sh. Guseinov, On Greens functions and positive solutions for boundary value problems on time scales, Journal of Computational and Applied Mathematics, 141, (2002), pp. 75-99.
Martin Bohner, Svetlin G. Georgiev, Multivariable Dynamic Calculus on Time Scales, Springer International Publishing Switzerland (2016).
Martin Bohner, Allan Peterson, Dynamic Equations on Time Scales An Introduction with Applications, Birkhauser Boston, (2001).
Martin Bohner, Allan Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser Boston, (2003).
Frank E. Burk, A Garden of Integrals, The Mathematical Association of America, 31, (2007).
G. Sh. Guseinov and B. Kaymakcalan, Basics of Riemann Delta and Nabla Integration on Time Scales, Journal of Difference Equations and Applications, 8 (11), (2002), pp. 1001-1017.
G. Sh. Guseinov, Integration on time scales, Journal of Mathematical Analysis and Applications, 285 , (2003), pp. 107-127.
S. Hilger, Analysis on Measure Chains- A unified approach to continuous and discrete calculus, Results in Mathematics, 18, (1990).
S. Hilger, Differential and Difference Calculus- Unified!, Nonlinear Analysis, Theory, Methods & Applications, 30(5), (1997), pp. 2683-2694.
Agnieszka B. Malinowska, Delfim F.M. Torres, The diamond-alpha Riemann integral and meanvalue theorems on time scales, Dynamic Systems and Applications , (2008), pp. 1-14.
James W. Rogers Jr., Qin Sheng, Notes on the diamond-a dynamic derivative on time scales, Journal of Mathematical Analysis and Applications, 326, (2007), pp. 228-241.
Q. Sheng, M. Fadag, J. Henderson, and J.M. Davis, An exploration of combined dynamic derivatives on time scales and their applications, Nonlinear Analysis: Real World Applications, 7 (2006), pp. 395-413.
Q. Sheng, A view of dynamic derivatives on time scales from approximations, Journal of Difference Equations and Applications, 11(1), (2005), pp. 63-81.
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