Results 31 to 40 of about 2,240 (300)
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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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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Results on Katugampola Fractional Derivatives and Integrals
International Journal of Analysis and Applications, 2023 In this paper, we introduce and develop a new definitions for Katugampola derivative and Katugampola integral. In particular, we defined a (left) fractional derivative starting from a of a function f of order α∈(m-1, m] and a (right) fractional derivative terminating at b, where m ∈ N.
Iqbal H. Jebril +4 more
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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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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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Fractional integration and the hyperbolic derivative [PDF]
Bulletin of the Australian Mathematical Society, 1988 We improve S. Yamashita's hyperbolic version of the well-known Hardy-Littlewood theorem. Let f be holomorphic and bounded by one in the unit disc D. If (f#)p has a harmonic mojorant in D for some p, p > 0, then so does σ(f)q for all q, 0 < q < ...
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On the Theory of Fractional Calculus in the Pettis-Function Spaces
Journal of Function Spaces, 2018 Throughout this paper, we outline some aspects of fractional calculus in Banach spaces. Some examples are demonstrated. In our investigations, the integrals and the derivatives are understood as Pettis integrals and the corresponding derivatives.
Hussein A. H. Salem
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k-Weyl fractional derivative, integral and integral transform
International Journal of Contemporary Mathematical Sciences, 2013 In this paper we define a new fractional derivative in the k-calculus context, the k-Weyl fractional derivative. Also we study the action of Laplace and Stieltjes Transforms on the new fractional operator and the k-Weyl Fractional Integral operator introduced by Romero, Cerutti, Dorrego (cf. [7]).
L. G. Romero, L. L. Luque
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A new Generalized fractional derivative and integral
, 2017 In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional derivative such as Product Rule, Quotient Rule, Chain Rule, Roll's Theorem and Mean Value Theorem.
AKKURT, Abdullah +2 more
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