Fractional Versions of the Fundamental Theorem of Calculus

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References

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[4] J. A. Tenreiro Machado, V. Kiryakova and F. Mainardi, “A Poster about the Recent History of Fractional Calculus,” Fractional Calculus & Applied Analysis, Vol. 13, No. 3, 2010, pp. 329-334.

[5] J. A. Tenreiro Machado, V. Kiryakova and F. Mainardi, “A Poster about the Old History of Fractional Calculus,” Fractional Calculus & Applied Analysis, Vol. 13, No. 4, 2010, pp. 447-454.

[6] J. A. Tenreiro Machado, V. Kiryakova and F. Mainardi, “Recent History of Fractional Calculus,” Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 3, 2011, pp. 1140-1153.
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[14] H. Vic Dannon, “The Fundamental Theorem of the Fractional Calculus and the Meaning of Fractional Derivatives,” Gauge Institute Journal, Vol. 5, No. 1, 2009, pp. 1-26.

[15] N. Heymans and I. Podlubny, “Physical Interpretation of Initial Conditions for Fractional Differential Equations with Riemann-Liouville Fractional Derivative,” Rheologica Acta, Vol. 45, No. 5, 2006, pp. 765-772.
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[16] I. Podlubny, “Geometric and Physical Interpretation of Fractional Integral and Fractional Differentiation,” Journal of Fractional Calculus & Applied Analysis, Vol. 5, No. 4, 2002, pp. 367-386.

[17] A. Cabada and G. Wang, “Positive Solutions of Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions,” Journal of Mathematical Analysis and Applications, Vol. 389, No. 1, 2012, pp. 403-411.
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[18] R. Figueiredo Camargo, “Fractional Calculus and Applications (in Portuguese)” Doctoral Thesis, UNICAMP, Campinas, 2009.

[19] J. A. Tenreiro Machado, “Discrete-Time Fractional-Order Controllers,” Journal of Fractional Calculus & Applied Analysis, Vol. 4, No. 1, 2001, pp. 47-66.

[20] R. Figueiredo Camargo, E. Capelas de Oliveira and J. Vaz Jr., “On the Generalized Mittag-Leffler Function and Its Application in a Fractional Telegraph Equation,” Mathematical Physsics, Analysis & Geometry, Vol. 15, No. 1, 2012, pp. 1-16. doi:10.1007/s11040-011-9100-8

[21] F. Silva Costa and E. Capelas de Oliveira, “Fractional Wave-Diffusion Equation with Periodic Conditions,” Journal of Mathematical Physics, Vol. 53, 2012, Article ID: 123520. doi:10.1063/1.4769270

[22] H. Jafari and S. Momani, “Solving Fractional Diffusion and wave Equations by Modified Homotopy Perturbation Method,” Physics Letters A, Vol. 370, No. 5-6, 2007, pp. 388-396. doi:10.1016/j.physleta.2007.05.118

[23] E. Contharteze Grigoletto, “Fractional Differential Equations and the Mittag-Leffler Functions (in Portuguese),” Ph.D. Thesis, UNICAMP, Campinas, to Appear.