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AIMS Mathematics, 2022 Riemann-Liouville fractional differential equations with impulses are useful in modeling the dynamics of many real world problems. It is very important that there are good and consistent theoretical proofs and meaningful results for appropriate problems.
Ravi Agarwal +2 more
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On a Nonlocal Problem for Mixed-Type Equation with Partial Riemann-Liouville Fractional Derivative
Fractal and Fractional, 2022 The present paper presents a study on a problem with a fractional integro-differentiation operator in the boundary condition for an equation with a partial Riemann-Liouville fractional derivative. The unique solvability of the problem is proved.
M. Ruziev, R. Zunnunov
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A new Definition of Fractional Derivative and Fractional Integral [PDF]
Kirkuk Journal of Science, 2018 In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed.
Ahmed M. Kareem
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Fractional Sobolev Spaces via Riemann-Liouville Derivatives [PDF]
Journal of Function Spaces and Applications, 2013 Using Riemann-Liouville derivatives, we introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones. Next, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and compactness of some imbeddings ...
Dariusz Idczak, Stanisław Walczak
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Mathematical Modelling and Analysis, 2017 This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first.
Fei Wang, Yongqing Yang
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Fractional boundary value problems with Riemann-Liouville fractional derivatives [PDF]
Advances in Difference Equations, 2015 In this paper, by employing two fixed point theorems of a sum operators, we investigate the existence and uniqueness of positive solutions for the following fractional boundary value problems: $-D_{0+}^{\alpha}x(t)=f(t, x(t),
Caozong Cheng, Jingjing Tan
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Approximation with Riemann-Liouville fractional derivatives [PDF]
Studia Universitatis Babes-Bolyai Matematica, 2019 n this article we study quantitatively with rates the pointwise convergence of a sequence of positive sublinear operators to the unit operator over continuous functions. This takes place under low order smothness,less than one, of the approximated function and it is expressed via the left and right Riemann-Liouville fractional derivatives of it.
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On a certain extension of the Riemann-Liouville fractional derivative operator [PDF]
arXiv: Classical Analysis and ODEs, 2018 15
Nisar Sooppy Kottakkaran Sooppy +3 more
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Solution of Fractional Order Equations in the Domain of the Mellin Transform
Journal of Nigerian Society of Physical Sciences, 2019 This paper presents the Mellin transform for the solution of the fractional order equations. The Mellin transform approach occurs in many areas of applied mathematics and technology.
Sunday Emmanuel Fadugba
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Analysis of fractional differential systems involving Riemann Liouville fractional derivative
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2020 This paper is devoted to studying the multiple positive solutions for a system of nonlinear fractional boundary value problems. Our analysis is based upon the Avery Peterson fixed point theorem. in addition, we include an example for the demonstration of our main result.
Batik, Songül, Deren, Fulya Yörük
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