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Incomplete Caputo fractional derivative operators
Advances in Difference Equations, 2018 The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types of incomplete hypergeometric functions and obtain their integral ...
Mehmet Ali Özarslan, Ceren Ustaoglu
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Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales [PDF]
Abstract and Applied Analysis, 2015 The definition of Caputo fractional derivative is given and some of its properties are discussed in detail. After then, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Caputo
Jiang Zhu, Ling Wu
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International Journal of Numerical Methods and Applications, 2018 Summary: In this paper, linear fractional Schrödinger equation is studied by using compact finite differences method. The fractional part of the equation is worked by applying Caputo fractional derivative definition. In the solution of the problem, finite differences discretization along the time, and fifth-order compact finite differences scheme along
Er, Neslihan +2 more
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Existence and Stability of a Caputo Variable-Order Boundary Value Problem
Journal of Mathematics, 2021 In this study, we investigate the existence of a solution to the boundary value problem (BVP) of variable-order Caputo-type fractional differential equation by converting it into an equivalent standard Caputo (BVP) of the fractional constant order with ...
Amar Benkerrouche +3 more
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Analysis and Modeling of Fractional-Order Buck Converter Based on Riemann-Liouville Derivative
IEEE Access, 2019 In previous studies, researchers used the fractional definition of Caputo to study fractional-order power converter. However, it is found that the model based on Caputo fractional definition is inconsistent with the actual situation.
Zhihao Wei, Bo Zhang, Yanwei Jiang
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On Caputo
IEEE Access, 2019 This paper studies the k-fractional analogue of the Caputo fractional derivatives, their properties, and applications. A convolution of two functions instead of the product is analyzed by means of Caputo k-fractional derivatives.
Asif Waheed +5 more
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Journal of Function Spaces, 2020 In this article, radial basis function collocation scheme is adopted for the numerical solution of fractional partial differential equations. This method is highly demanding because of its meshless nature and ease of implementation in high dimensions and
Mehnaz Shakeel +5 more
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Scientific Reports, 2022 In this paper, we have been study a hybrid nanofluid over an exponentially oscillating vertical flat plate. Therefore the fractional derivatives definition of Caputo–Fabrizio approach is applied to transform the classical model for this hybrid nanofluid ...
Sami Ul Haq +5 more
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Fractional Probability Theory of Arbitrary Order
Fractal and Fractional, 2023 A generalization of probability theory is proposed by using the Riemann–Liouville fractional integrals and the Caputo and Riemann–Liouville fractional derivatives of arbitrary (non-integer and integer) orders. The definition of the fractional probability
Vasily E. Tarasov
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Alexandria Engineering Journal, 2020 The present paper consider a newly introduced operator known as fractal-fractional where the fractional operator considered is Caputo-Fabrizio. We consider a competition system and propose the field data of banks for 2004–2014 of Indonesia banks of the ...
Abdon Atangana +2 more
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