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Applications of fractional calculus
Mehdi Dalir,Majid Bashour +1 more
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This article is published in Applied mathematical sciences.The article was published on 2010-01-01 and is currently open access. It has received 503 citations till now. The article focuses on the topics: Fractional calculus.read more
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Properties of a New Fractional Derivative without Singular Kernel
TL;DR: In this article, the fractional integral corresponding to the new concept of fractional derivative was introduced, and some related fractional differential equations were studied in the context of the FDE.
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Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel
TL;DR: A fractional calculus with an integral operator which contains the following family of generalized Mittag-Leffler functions: E"@a","@b^@c^,^@k(z), (@l)"@n being the familiar Pochhammer symbol.
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Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
TL;DR: A new formula expressing explicitly the derivatives of shifted Chebyshev polynomials of any degree and for any fractional-order in terms of shiftedChebyshevs themselves is state and prove.
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A tau approach for solution of the space fractional diffusion equation
Abbas Saadatmandi,Mehdi Dehghan +1 more
TL;DR: In this paper, an approximation technique based on the shifted Legendre-tau idea is presented to solve a class of initial-boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain.
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Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay
TL;DR: The problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed with the help of the stability theory.