Displaying similar documents to “An effective method for solving fractional integro-differential equations.”

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

Luchko, Yury, Trujillo, Juan (2007)

Fractional Calculus and Applied Analysis

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2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05 The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones. Whereas the Riemann-Liouville definition of a fractional derivative is usually employed in mathematical texts and not so frequently in applications, and the Grünwald-Letnikov definition – for numerical approximation of both Caputo and Riemann-Liouville...

Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

Mainardi, Francesco, Gorenflo, Rudolf (2007)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05, The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classica theory of linear viscoelasticity, we contrast these two types of fractiona derivatives in their...

Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Saxena, R., Saxena, Ravi, Kalla, S. (2010)

Fractional Calculus and Applied Analysis

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Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10. The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function....

A Fractional LC − RC Circuit

Ayoub, N., Alzoubi, F., Khateeb, H., Al-Qadi, M., Hasan (Qaseer), M., Albiss, B., Rousan, A. (2006)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05 We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution...

Hamilton’s Principle with Variable Order Fractional Derivatives

Atanackovic, Teodor, Pilipovic, Stevan (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo We propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler–Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined...