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Applications of Fractional Calculus
Anita Alaria,Arif Khan +1 more
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Explicit formulas and graphs of few special functions are derived in this article on the basis of various definitions of various fractional derivatives and their applications are also reviewed in the paper, where the authors also review their applications.Abstract:
Explicit formula and graphs of few special functions are derived in the paper on the basis of various definitions of various fractional derivatives and various fractional integrals. Their applications are also reviewed in the paper.read more
Citations
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New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations
TL;DR: In this article, the authors considered integro-differential equations involving Atangana-Baleanu fractional derivatives which contain the generalized Mittag-Leffler functions in their kernels and examined the existence and uniqueness of solutions to such equations in Banach spaces.
Journal ArticleDOI
Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm
TL;DR: The reproducing kernel algorithm is introduced for treating classes of time-fractional partial differential equations subject to Robin boundary conditions with parameters derivative arising in fluid flows, fluid dynamics, groundwater hydrology, conservation of energy, heat conduction and electric circuit.
Journal ArticleDOI
Linear fractional order controllers; A survey in the frequency domain
TL;DR: This paper helps beginners to get started rapidly and learn how to select, tune, approximate, discretize, and implement FO-controllers in the frequency domain.
Journal ArticleDOI
Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique
Pei-Ying Xiong,Hadi Jahanshahi,Raúl Alcaraz,Yu-Ming Chu,J. F. Gómez-Aguilar,Fawaz E. Alsaadi +5 more
TL;DR: Numerical results demonstrate the chattering-free and effective performance of the proposed control method for uncertain systems in the presence of unknown time-varying external disturbances.
Journal ArticleDOI
Finite Difference/Finite Element Methods for Distributed-Order Time Fractional Diffusion Equations
Weiping Bu,Aiguo Xiao,Wei Zeng +2 more
TL;DR: To improve the convergence rate in time, the weighted and shifted Grünwald difference method is used and a higher order finite difference scheme of the Caputo fractional derivative is developed to improve the time convergence rate of the methods.
References
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Journal ArticleDOI
Applications of Fractional Calculus to the Theory of Viscoelasticity
TL;DR: The relation entre le calcul fractionnaire and the theory of l'equation integrale d'Abel for les materiaux a memoire is discussed in this paper.
Journal ArticleDOI
Application of Fractional Calculus to Fluid Mechanics
Vladimir V. Kulish,José L. Lage +1 more
TL;DR: In this paper, the Laplace transform method and fractional calculus of arbitrary (noninteger) differentiation were applied to the solution of time-dependent, viscous-diffusion fluid mechanics problems.
Journal ArticleDOI
Fractional Calculus in Bioengineering, Part 2
TL;DR: By expanding the range of mathematical operations to include fractional calculus, the authors can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner.
Journal ArticleDOI
New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations
TL;DR: In this article, the authors considered integro-differential equations involving Atangana-Baleanu fractional derivatives which contain the generalized Mittag-Leffler functions in their kernels and examined the existence and uniqueness of solutions to such equations in Banach spaces.
Journal ArticleDOI
Numerical solutions for the Robin time-fractional partial differential equations of heat and fluid flows based on the reproducing kernel algorithm
TL;DR: The reproducing kernel algorithm is introduced for treating classes of time-fractional partial differential equations subject to Robin boundary conditions with parameters derivative arising in fluid flows, fluid dynamics, groundwater hydrology, conservation of energy, heat conduction and electric circuit.