Displaying similar documents to “A Poster about the Recent History of Fractional Calculus”

A Poster about the Old History of Fractional Calculus

Tenreiro Machado, J., Kiryakova, Virginia, Mainardi, Francesco (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22 The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.

Theorems on some families of fractional differential equations and their applications

Gülçin Bozkurt, Durmuş Albayrak, Neşe Dernek (2019)

Applications of Mathematics

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We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for...

On a Differential Equation with Left and Right Fractional Derivatives

Atanackovic, Teodor, Stankovic, Bogoljub (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05 We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational principles with fractional derivatives. We reduce the problem to a Fredholm integral equation and construct a solution in the space of continuous functions. Two competing approaches in formulating differential equations...

On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)

Małgorzata Klimek (2011)

Banach Center Publications

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One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.

Professor Rudolf Gorenflo and his Contribution to Fractional Calculus

Luchko, Yury, Mainardi, Francesco, Rogosin, Sergei (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary This paper presents a brief overview of the life story and professional career of Prof. R. Gorenflo - a well-known mathematician, an expert in the field of Differential and Integral Equations, Numerical Mathematics, Fractional Calculus and Applied Analysis, an interesting conversational partner, an experienced colleague, and a real friend. Especially his role in the modern Fractional...