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The origin and developments of Kurzweil’s generalized Riemann integral
The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further...
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The Π-Riemann Integral
In Chap. 2 we introduce the Π–Riemann integral and discuss its basic properties. In particular, we observe that even though the Riemann sums of an...
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History of Mathematics Illuminates Philosophy of Mathematics: Riemann, Weierstrass and Mathematical Understanding
This paper explores two respects in which a study of the history of mathematics can enrich the philosophy of mathematics. First, central concepts in...
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The Butzer-Kozakiewicz article on Riemann derivatives of 1954 and its influence
The article on Riemann derivatives by P. L. Butzer and W. Kozakiewicz of 1954 was the basis to generalizations of the classical scalar-valued...
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On the monotonicity of left and right Riemann sums
This paper is dedicated to proving general theorems about the monotonicity of left and right Riemann sums, a problem first raised by Fejér in 1950....
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Riemann and His Time
This is an extended version of a lecture given in Varese on 23/09/2021 in occasion of the awarding of the Riemann prize to Terence Tao.
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A generalization of the Riemann–Siegel formula
The celebrated Riemann–Siegel formula compares the Riemann zeta function on the critical line with its partial sums, expressing the difference...
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Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems
We are concerned with global solutions of multidimensional (M-D) Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on...
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Analysis of Q-Fractional Implicit Differential Equation with Nonlocal Riemann–Liouville and Erdélyi-Kober Q-Fractional Integral Conditions
This manuscript aims to present the existence, uniqueness, and various kinds of Ulam’s stability for the solution of the implicit q -fractional...
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Curve shortening flow on Riemann surfaces with conical singularities
We study the curve shortening flow on Riemann surfaces with finitely many conformal conical singularities. If the initial curve is passing through...
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Delay-dependent and order-dependent asymptotic stability conditions for Riemann–Liouville fractional-order systems with time delays
In this paper, the asymptotic stability problem for Riemann–Liouville fractional-order systems with time delays is investigated. First, a new...
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Integral Transforms and Special Functions
This chapter provides the essential mathematical tools to be used in the subsequent chapters, and is intended to make the book as self-contained as...
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Optimal feedback control for a class of fractional evolution equations with history-dependent operators
In this paper, we will study optimal feedback control problems derived by a class of Riemann-Liouville fractional evolution equations with...
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The Integral
The idea of “integration” is as old as mathematics: it starts with the necessity of measuring areas delimited by curves. The problem is that our...
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The Integral
In Sect. 2.1, we recall the definition of the Cauchy integral of a continuous function with compact support. Four basic properties satisfied by the...
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Integral operators and fractional integrals on Cesáro-Morrey function spaces
In this paper, we extend the study of the Cesáro function spaces to the Cesáro-Morrey function spaces. We establish a general principle on the...
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Padé approximants on Riemann surfaces and KP tau functions
The paper has two relatively distinct but connected goals; the first is to define the notion of Padé approximation of Weyl–Stiltjes transforms on an...
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On the study of the positive solutions of a BVP under \(\psi \)-Riemann–Liouville fractional derivative via upper and lower solution method
In this paper, we study the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional integro-differential...