# Applications of Fractional Calculus

@inproceedings{Dalir2010ApplicationsOF, title={Applications of Fractional Calculus}, author={Mehdi Dalir and Majid Bashour}, year={2010} }

Different definitions of fractional derivatives and fractional Integrals (Differintegrals) are considered. By means of them explicit formula and graphs of some special functions are derived. Also we reviw some applications of the theory of fractional calculus.

#### 315 Citations

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A numerical technique based on the Cauchy integral formula of complex analysis has been employed for evaluating the integrals and derivatives of fractional orders of an analytic function. The method… Expand

Generalizations of some fractional integral inequalities via generalized Mittag-Leffler function

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Some general integral inequalities containing generalized Mittag-Leffler function and some already known integral inequalities have been produced as special cases are obtained. Expand

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- Advances in Difference Equations
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In this paper, by means of the Krasnoselskii fixed point theorem, the existence of solutions for a boundary value problem of nonlinear sequential fractional integro-differential equations are… Expand

More properties of the proportional fractional integrals and derivatives of a function with respect to another function

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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… Expand

Some applications of fractional calculus for analytic functions

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- TURKISH JOURNAL OF MATHEMATICS
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For analytic functions f (z) in the class An, fractional calculus (fractional integrals and fractional derivatives) D z f (z) of order λ are introduced. Applying D z f (z) for f (z) ∈ An, we… Expand

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An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

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- TheScientificWorldJournal
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It is shown how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type, and how the efficiency of the approximation method is illustrated with examples. Expand

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