Displaying similar documents to “Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative”

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....

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...

Fractional Integration and Fractional Differentiation of the M-Series

Sharma, Manoj (2008)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 33C60, 44A15 In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note...

A Brief Story about the Operators of the Generalized Fractional Calculus

Kiryakova, Virginia (2008)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 26A33, 33C60, 44A20 In this survey we present a brief history and the basic ideas of the generalized fractional calculus (GFC). The notion “generalized operator of fractional integration” appeared in the papers of the jubilarian Prof. S.L. Kalla in the years 1969-1979 when he suggested the general form of these operators and studied examples of them whose kernels were special functions as the Gauss and generalized hypergeometric functions,...

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Stojanović, Mirjana (2010)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05. We give the proofs of the existence and regularity of the solutions in the space C^∞ (t > 0;H^(s+2) (R^n)) ∩ C^0(t ≧ 0;H^s(R^n)); s ∊ R, for the 1-term, 2-term,..., n-term time-fractional equation evaluated from the time fractional equation of distributed order with spatial Laplace operator Δx ...

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Garg, Mridula, Manohar, Pratibha (2010)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05. In the present paper we solve space-time fractional diffusion-wave equation with two space variables, using the matrix method. Here, in particular, we give solutions to classical diffusion and wave equations and fractional diffusion and wave equations with different combinations of time and space fractional derivatives. We also plot some graphs for these problems with the help of MATLAB routines. ...

Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Rossikhin, Yuriy, Shitikova, Marina (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 74D05, 26A33 In this paper, a comparative analysis of the models involving fractional derivatives of di®erent orders is given. Such models of viscoelastic materials are widely used in various problems of mechanics and rheology. Rabotnov's hereditarily elastic rheological model is considered in detail. It is shown that this model is equivalent to the rheological model involving fractional derivatives in the stress and strain with the orders...

Inhomogeneous Fractional Diffusion Equations

Baeumer, Boris, Kurita, Satoko, Meerschaert, Mark (2005)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05 Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analytic...

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...