Results 11 to 20 of about 2,492 (112)
On fractional calculus with general analytic kernels [PDF]
Applied Mathematics and Computation, 2019 Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions.
Arran Fernandez +2 more
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Nonlocal Probability Theory: General Fractional Calculus Approach
Mathematics, 2022 Nonlocal generalization of the standard (classical) probability theory of a continuous distribution on a positive semi-axis is proposed. An approach to the formulation of a nonlocal generalization of the standard probability theory based on the use of the general fractional calculus in the Luchko form is proposed.
Vasily E Tarasov
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Generalized integral inequalities for fractional calculus
Cogent mathematics & statistics, 2018 In this paper, we present a variety of integral inequalities in Lp and Lp, r spaces for the integral operator involving generalized Mittag-Leffler function in its kernel, Hilfer fractional derivative, generalized Riemann-Liouville and Riemann- Liouville k-fractional integral operators.
Iqbal, Sajid +2 more
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Fractional calculus and application of generalized Struve function [PDF]
SpringerPlus, 2016 A new generalization of Struve function called generalized Galué type Struve function (GTSF) is defined and the integral operators involving Appell's functions, or Horn's function in the kernel is applied on it. The obtained results are expressed in terms of the Fox-Wright function.
Kottakkaran Sooppy Nisar +2 more
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Fractional-Order Variational Calculus with Generalized Boundary Conditions [PDF]
Advances in Difference Equations, 2011 تقدم هذه الورقة شروط الأمثلية الضرورية والكافية للمشاكل المتغيرة الكسرية التي تنطوي على التكاملات الكسرية اليمنى واليسرى والمشتقات الكسرية المحددة بمعنى ريمان- ليوفيل مع لاغرانج اعتمادًا على نقاط النهاية الحرة. لتوضيح نهجنا، نناقش مثالين بالتفصيل.
Mohamed A. E. Herzallah +1 more
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Generalized Memory: Fractional Calculus Approach [PDF]
Fractal and Fractional, 2018 The memory means an existence of output (response, endogenous variable) at the present time that depends on the history of the change of the input (impact, exogenous variable) on a finite (or infinite) time interval. The memory can be described by the function that is called the memory function, which is a kernel of the integro-differential operator ...
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Fractional calculus of variations with a generalized fractional derivative [PDF]
Fractional Differential Calculus, 2016 Summary: In this paper, we introduce a generalization of the Hilfer-Prabhakar derivative and obtain the Euler-Lagrange equations and Hamiltonian formulation with respect to this fractional derivative in the theory of fractional calculus of variations. Also, we get a sufficient condition for optimality.
Askari, Hassan, Ansari, Alireza
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A Generalized Fractional Calculus of Variations
, 2013 This is a preprint of a paper whose final and definitive form will appear in Control and Cybernetics.
Odzijewicz, T. +2 more
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Fractional Calculus of the Generalized Mittag-Leffler Type Function [PDF]
International Scholarly Research Notices, 2014 We introduce and study a new function called R-function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the R-function and Saigo fractional calculus operators. Some results derived by Samko et al. (1993), Kilbas (2005), Kilbas and Saigo (1995), and Sharma and Jain (2009) are special cases of
Dinesh Kumar, Sunil Kumar
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General Fractional Calculus Operators of Distributed Order
Axioms, 2023 In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law ...
Mohammed Al-Refai, Yuri Luchko
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