Results 11 to 20 of about 56,789 (179)
Calculus of variations with fractional derivatives and fractional integrals [PDF]
Applied Mathematics Letters, 2009 We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
Ricardo Almeida, Delfim F. M. Torres
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Fractional calculus in mathematical oncology [PDF]
Scientific Reports, 2023 AbstractEven though, nowadays, cancer is one of the leading causes of death, too little is known about the behavior of this disease due to its unpredictability from one patient to another. Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage ...
Tudor Alinei-Poiana +2 more
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Fractional Calculus and the Future of Science [PDF]
Entropy, 2021 The invitation to contribute to this anthology of articles on the fractional calculus (FC) encouraged submissions in which the authors look behind the mathematics and examine what must be true about the phenomenon to justify the replacement of an integer-order derivative with a non-integer-order (fractional) derivative (FD) before discussing ways to ...
West BJ.
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Tempered fractional calculus [PDF]
Journal of Computational Physics, 2015 Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an ...
Jinghua Chen +2 more
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Calculus of Variations with Classical and Fractional Derivatives [PDF]
, 2010 We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the
Tatiana Odzijewicz, Delfim F. M. Torres
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Generalized fractional calculus with applications to the calculus of variations
Computers & Mathematics with Applications, 2012 Submitted 22-Dec-2011; revised 26-Jan-2012; accepted 27-Jan-2012; for publication in Computers and Mathematics with ...
Tatiana Odzijewicz +2 more
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Fractional calculus in pharmacokinetics [PDF]
Journal of Pharmacokinetics and Pharmacodynamics, 2017 We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the ...
Pantelis Sopasakis +3 more
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On Weyl fractional calculus [PDF]
Proceedings of the American Mathematical Society, 1979 The Weyl fractional calculus is applied in developing the Laplace transform of t q f ( t ) {t^q}f(t) , for all values of q. Also, a generalized Taylor’s formula in Weyl fractional calculus is established.
R. K. Raina, C. L. Koul
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Complexity and the Fractional Calculus [PDF]
Advances in Mathematical Physics, 2013 We study complex processes whose evolution in time rests on the occurrence of a large and random number of events. The mean time interval between two consecutive critical events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that supports the hypothesis that the Mittag-Leffler ...
Pramukkul, Pensri +4 more
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