fractional integrals and derivatives pdf

Fractional Integrals And Derivatives Pdf

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Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D. More generally, one can look at the question of defining a linear operator. Fractional differential equations, also known as extraordinary differential equations, [1] are a generalization of differential equations through the application of fractional calculus.

Antonio Bernardino de Almeida , Porto, Portugal.

Show all documents New Hermite-Hadamard inequalities via fractional integrals, whose absolute values of second derivatives is P-convex Abstract. In this research article, authors have established a general integral identity for Riemann- Liouville fractional integrals. Some new results related to the left-hand side of Hermite-Hadamard type integral inequalities utilizing this integral identity for the class of functions whose second derivatives at some power are P-convex are obtained. The presented results have some closely connection with [M.

Spectral approximations to the fractional integral and derivative

Preliminaries The spaces H x and H x p , The spaces L p and L p p Some special functions Integral transforms Riemann-Liouville Fractional Integrals and Derivatives The Abel integral equation On the solvability of the Abel equation in the space of integrable functions Definition of fractional integrals and derivatives and their simplest properties Fractional integrals and derivatives of complex order Fractional integrals of some elementary functions Fractional integration and differentiation as reciprocal operations Composition formulae. Connection with semigroups of operators Lizorkin's space of test functions. Schwartz's approach The case of the half-axis. The approach via the adjoint operator McBride's spaces The case of an interval Bibliographical Remarks and Additional Information to Chapter Historical notes Survey of other results relating to Tables of fractional integrals and derivatives Chapter 3 Further Properties of Fractional Integrals and Derivatives Compositions of Fractional Integrals and Derivatives with Weights Compositions of two one-sided integrals with power weights Compositions of two-sided integrals with power weights Compositions of several integrals with power weights Compositions with exponential and power-exponential weights Connection between Fractional Integrals and the Singular Operator The singular operator S The case of the whole line The case of an interval and a half-axis Some other composition relations Fractional Integrals of the Potential Type The real axis. The Riesz and Feller potentials On the "truncation" of the Riesz potential to the half-axis The case of the half-axis The case of a finite interval Functions Representable by Fractional Integrals on an Interval The Marchaud fractional derivative on an interval Characterization of fractional integrals of functions in L p Continuation, restriction and "sewing" of fractional integrals Characterization of fractional integrals of Holderian functions

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Metrics details. In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann—Liouville setting and the one in Caputo. In addition, we provide an integration by parts formulas related to the considered operators. For the last 30 years or more, some scientists have shown a great deal of interest in the field of fractional calculus which addresses the derivatives and integrals with any order. As a matter of fact, this interest has sprung out by the dint of the substantial results obtained when these scientists used the tools in this calculus in order to study some models from the real world [ 1 — 6 ]. One of the virtues of the classical fractional calculus is that there are a variety of derivatives and integrals.

Fractional Integrals and Derivatives: Theory and Applications

While we are building a new and improved webshop, please click below to purchase this content via our partner CCC and their Rightfind service. You will need to register with a RightFind account to finalise the purchase. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor JIF and impact rang SJR , launching the journal to top places of the ranking lists of Thomson Reuters and Scopus. EN English Deutsch. Your documents are now available to view. Confirm Cancel.

Fractional Calculus and Applied Analysis , 15 3 , pp. Open access copy at publisher website. In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.


PDF | We generalize the notions of the fractional q-integral and q-derivative by introducing variable lower limit of integration. We discuss some | Find, read and​.


FRACTIONAL INTEGRALS AND DERIVATIVES. Theory and Applications

Stefan Samko 28 Estimated H-index: View Paper. Add to Collection. Fractional integrals and derivatives on an interval fractional integrals and derivatives on the real axis and half-axis further properties of fractional integrals and derivatives other forms of fractional integrals and derivatives fractional integrodifferentiation of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations fo the first kind with special function kernels applications to differential equations. Paper References 0 Citations

A systematic and comprehensive exposition of classical and modern results in the theory of fractional integrals and their applications. Various aspects of this theory, such as functions of one and several variables and periodical and non-periodical cases, are studied. Read more

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Spectral approximations to the fractional integral and derivative

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