Journal ArticleDOI
On fractional thermoelasticity
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In this article, two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained.Abstract:
Two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained, uniqueness an...read more
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A new collection of real world applications of fractional calculus in science and engineering
TL;DR: This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus that will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool.
Journal ArticleDOI
On some new properties of fractional derivatives with Mittag-Leffler kernel
Dumitru Baleanu,Arran Fernandez +1 more
TL;DR: A new formula for the fractional derivative with Mittag-Leffler kernel is established, in the form of a series of Riemann–Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier to handle for certain computational purposes.
Journal ArticleDOI
The Prabhakar or three parameter Mittag-Leffler function: Theory and application
Roberto Garra,Roberto Garrappa +1 more
TL;DR: The Prabhakar function, a three parameter Mittag–Leffler function, is investigated and the asymptotic expansion for large arguments is investigated in the whole complex plane and, with major emphasis, along the negative semi-axis.
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Generalized thermo-viscoelasticity with memory-dependent derivatives
TL;DR: In this article, a generalized thermo-viscoelasticity theory with memory-dependent derivatives is constructed, and the governing coupled equations with time-delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to one-dimensional problem of a half-space.
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The Chronicles of Fractional Calculus
TL;DR: In this article, a survey analyzes and measures the evolution that occurred during the last five decades in the light of books, journals and conferences dedicated to the theory and applications of fractional calculus, dealing with operations of integration and differentiation of arbitrary (fractional) order and their generalizations.
References
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Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Book
Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
Book
The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order
Keith B. Oldham,Jerome Spanier +1 more
TL;DR: In the beginning, when having significantly cash, why don't you attempt to acquire something basic in the beginning? That's something that will guide you to understand even more in the region of the globe, experience, some places, history, amusement, and a lot more as discussed by the authors.
Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.