Editorial for Special Issue “Fractional Calculus and Special Functions with Applications”
Fractal and Fractional, 2021 The study of fractional integrals and fractional derivatives has a long history, and they have many real-world applications due to their properties of interpolation between operators of integer order [...]
Mehmet Ali Özarslan +2 more
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Fractional Sums and Differences with Binomial Coefficients
Discrete Dynamics in Nature and Society, 2013 In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives.
Thabet Abdeljawad +3 more
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Volterra integral equations and fractional calculus: Do neighbouring solutions intersect? [PDF]
, 2012 This is the author's PDF version of an article published in Journal of Integral Equations and Applications. The definitive version is available at rmmc.asu.edu/jie/jie.html.This journal article considers the question of whether or not the solutions to ...
Diethelm, Kai, Ford, Neville J.
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Hadamard fractional integrals and derivatives with respect to functions
CQD Revista Eletrônica Paulista de Matemática, 2022 In this article, we study generalized fractional derivatives and integrals that contain kernels a generalized logarithm depending on a positive continuous function increasing.
Ana Paula Perovano +1 more
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Taylor’s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels
Axioms, 2022 We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean
Houssine Zine +3 more
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On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals [PDF]
Sahand Communications in Mathematical Analysis, 2021 In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded .
Huseyin Budak +2 more
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The properties of Bessel-type fractional derivatives and integrals [PDF]
, 2016 The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis.
Gorty, V. R. Lakshmi
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On the 1st-Level General Fractional Derivatives of Arbitrary Order
Fractal and Fractional, 2023 In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and ...
Yuri Luchko
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Fractional variational problems depending on indefinite integrals
, 2012 We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor +8 more
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Operational Calculus for the General Fractional Derivatives of Arbitrary Order
Mathematics, 2022 In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari +2 more
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