An Introduction to Paraconsistent Integral Differential Calculus: With Application Examples

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References

[1] Da Costa, N.C.A. (2000) Paraconsistent Mathematics. In: Batens, D., Mortensen, C., Priest, G. and Bendegen van, J.P., Eds., I World Congress on Paraconsistency1998 Ghent, Belgium, Frontiers in Paraconsistent Logic: Proceedings, King’s College Publications, London, 165-179.

[2] Jas’kowski, S. (1969) Propositional Calculus for Contradictory Deductive Systems. Studia Logica, 24, 143-157.

http://dx.doi.org/10.1007/BF02134311

[3] Da Costa, N.C.A. (1986) On Paraconsistent Set Theory. Logique et Analyse, 115, 361-371.

[4] Da Silva Filho, J.I., Lambert-Torres, G. and Abe, J.M. (2010) Uncertainty Treatment Using Paraconsistent Logic: Introducing Paraconsistent Artificial Neural Networks. IOS Press, Amsterdam, 328.

[5] Da Silva Filho, J.I. (2011) Paraconsistent Annotated Logic in Analysis of Physical Systems: Introducing the Paraquantum γψ Gamma Factor. Journal of Modern Physics, 2, 1455-1469.

http://dx.doi.org/10.4236/jmp.2011.212180

[6] Da Silva Filho, J.I. (2012) Analysis of the Emissions Spectral line of the Paraquantum with Hydrogen Atom. Journal of Modern Physics, 3, 233-254.

http://dx.doi.org/10.4236/jmp.2012.33033

[7] Da Silva Filho, J.I. (2012) An Introductory Study of the Hydrogen Atom with Paraquantum Logic. Journal of Modern Physics, 3, 312-333.

http://dx.doi.org/10.4236/jmp.2012.34044

[8] Da Silva Filho, J.I. (2011) Paraconsistent Annotated Logic in analysis of Physical Systems: Introducing the Paraquantum hψ Factor of Quantization. Journal of Modern Physics, 2, 1397-1409.

http://dx.doi.org/10.4236/jmp.2011.211172

[9] Stroyan, K.D. and Luxemburg, W.A.J. (1976) Introduction to the Theory of Infinitesimals. Academic Press, New York.

[10] Bell, J.L. (1998) A Primer of Infinitesimal Analysis. Cambridge University Press, Cambridge.

[11] Baron, M.E. (1969) The Origins of the Infinitesimal Calculus. Pergamon Press, Hungary.

[12] Keisler, H.J. (1976) Elementary Calculus: An Infinitesimal Approach. 1st Edition, Prindle, Weber & Schmidt, Boston.

[13] Diethelm, K. and Ford, N. (2004) Multi-Order Fractional Differential Equations and Their Numerical Solution. Applied Mathematics and Computation, 154, 621-640.

http://dx.doi.org/10.1016/S0096-3003(03)00739-2

[14] Pl Tipler, A. and Llewellyn, R.A. (2007) Modern Physics. 5th Edition, W. H. Freeman and Company, New York.

[15] Kleene, S.C. (1952) Introduction to Metamathematics. North Holland/Van Nostrand, Amsterdam/New York.