New theories and applications of tempered fractional differential equations
Sign Up to like & getrecommendations! Published in 2021 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-021-06628-4
Abstract: In this paper, we develop theories, properties and applications of a new technique in tempered fractional calculus called the Tempered Fractional Natural Transform Method. This method can be used to solve a myriad of problems… read more here.
Keywords: fractional natural; tempered fractional; method; natural transform ... See more keywords
Numerical methods for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion
Sign Up to like & getrecommendations! Published in 2019 at "Numerical Algorithms"
DOI: 10.1007/s11075-019-00800-z
Abstract: In this paper, we study the numerical schemes for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion. The main challenges of the numerical schemes come from the singularity… read more here.
Keywords: planck equation; fokker planck; tempered fractional; fractional brownian ... See more keywords
A computationally efficient method for tempered fractional differential equations with application
Sign Up to like & getrecommendations! Published in 2018 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-017-0522-1
Abstract: This paper investigates the numerical approximation of the tempered fractional integral by using the Sinc-collocation scheme. The algorithm is extended to solve a class of tempered fractional differential equations that converges to the solution with… read more here.
Keywords: efficient method; tempered fractional; fractional differential; differential equations ... See more keywords
Numerical schemes for a class of tempered fractional integro-differential equations
Sign Up to like & getrecommendations! Published in 2020 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2020.05.026
Abstract: Abstract For a class of tempered fractional integro-differential equation of the Caputo type, a comparative study of three numerical schemes is presented in this paper. The schemes discussed are Linear, Quadratic and Quadratic-Linear schemes. Four… read more here.
Keywords: integro differential; tempered fractional; numerical schemes; fractional integro ... See more keywords
Tempered fractional Poisson processes and fractional equations with Z-transform
Sign Up to like & getrecommendations! Published in 2018 at "Stochastic Analysis and Applications"
DOI: 10.1080/07362994.2020.1748056
Abstract: Abstract In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson process and space-fractional Poisson processes. We also… read more here.
Keywords: poisson processes; tempered fractional; fractional equations; poisson ... See more keywords
TEMPERED FRACTIONAL CALCULUS ON TIME SCALE FOR DISCRETE-TIME SYSTEMS
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DOI: 10.1142/s0218348x21400338
Abstract: The fractional derivative holds historical dependence or non-locality and it becomes a powerful tool in many real-world applications. But it also brings error accumulation of the numerical solutions as well as the theoretical analysis since… read more here.
Keywords: tempered fractional; time; fractional calculus; time scale ... See more keywords
Tempered Mittag–Leffler Stability of Tempered Fractional Dynamical Systems
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Problems in Engineering"
DOI: 10.1155/2020/7962542
Abstract: Due to finite lifespan of the particles or boundedness of the physical space, tempered fractional calculus seems to be a more reasonable physical choice. Stability is a central issue for the tempered fractional system. This… read more here.
Keywords: tempered mittag; tempered fractional; leffler stability; stability tempered ... See more keywords
Second-order numerical methods for the tempered fractional diffusion equations
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Difference Equations"
DOI: 10.1186/s13662-019-2417-5
Abstract: In this paper, a class of second-order tempered difference operators for the left and right Riemann–Liouville tempered fractional derivatives is constructed. And a class of second-order numerical methods is presented for solving the space tempered… read more here.
Keywords: order numerical; fractional diffusion; order; tempered fractional ... See more keywords
Tempered Fractional Trapezium Inequalities
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DOI: 10.3390/axioms11110624
Abstract: The main objective of this paper is to derive some new fractional analogs of trapezium-like inequalities essentially using the class of preinvex functions and the concepts of tempered fractional integrals. We discuss some special cases… read more here.
Keywords: trapezium inequalities; trapezium; tempered fractional; fractional trapezium ... See more keywords
On the Generalized Hermite-Hadamard Inequalities via the Tempered Fractional Integrals
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DOI: 10.3390/sym12040595
Abstract: Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of… read more here.
Keywords: generalized hermite; tempered fractional; fractional integrals; hadamard inequalities ... See more keywords
Bilateral Tempered Fractional Derivatives
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DOI: 10.3390/sym13050823
Abstract: The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and shows that it cannot… read more here.
Keywords: tempered fractional; fractional derivatives; bilateral tempered;