Cauchy integral on time scales: constructive sense
DOI:
https://doi.org/10.5269/bspm.64192Resumo
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
Referências
[1] Ravi P. Agarwal and Martin Bohner, Basic Calculus on Time Scales and some of its Applications, Results in Mathematics, 35, (1999), pp. 3-22.
[2] 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.
[3] Martin Bohner, Svetlin G. Georgiev, Multivariable Dynamic Calculus on Time Scales, Springer International Publishing Switzerland (2016).
[4] Martin Bohner, Allan Peterson, Dynamic Equations on Time Scales An Introduction with Applications, Birkhauser Boston, (2001).
[5] Martin Bohner, Allan Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser Boston, (2003).
[6] Frank E. Burk, A Garden of Integrals, The Mathematical Association of America, 31, (2007).
[7] 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.
[8] G. Sh. Guseinov, Integration on time scales, Journal of Mathematical Analysis and Applications, 285 , (2003), pp. 107-127.
[9] S. Hilger, Analysis on Measure Chains- A unified approach to continuous and discrete calculus, Results in Mathematics, 18, (1990).
[10] S. Hilger, Differential and Difference Calculus- Unified!, Nonlinear Analysis, Theory, Methods & Applications, 30(5), (1997), pp. 2683-2694.
[11] 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.
[12] 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.
[13] 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.
[14] Q. Sheng, A view of dynamic derivatives on time scales from approximations, Journal of Difference Equations and Applications, 11(1), (2005), pp. 63-81.
[2] 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.
[3] Martin Bohner, Svetlin G. Georgiev, Multivariable Dynamic Calculus on Time Scales, Springer International Publishing Switzerland (2016).
[4] Martin Bohner, Allan Peterson, Dynamic Equations on Time Scales An Introduction with Applications, Birkhauser Boston, (2001).
[5] Martin Bohner, Allan Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser Boston, (2003).
[6] Frank E. Burk, A Garden of Integrals, The Mathematical Association of America, 31, (2007).
[7] 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.
[8] G. Sh. Guseinov, Integration on time scales, Journal of Mathematical Analysis and Applications, 285 , (2003), pp. 107-127.
[9] S. Hilger, Analysis on Measure Chains- A unified approach to continuous and discrete calculus, Results in Mathematics, 18, (1990).
[10] S. Hilger, Differential and Difference Calculus- Unified!, Nonlinear Analysis, Theory, Methods & Applications, 30(5), (1997), pp. 2683-2694.
[11] 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.
[12] 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.
[13] 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.
[14] 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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2024-05-17
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