Displaying similar documents to “Inhomogeneous Fractional Diffusion Equations”

Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Nikolova, Yanka, Boyadjiev, Lyubomir (2010)

Fractional Calculus and Applied Analysis

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Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12. The method of integral transforms based on using a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problem for the time-space fractional diffusion equation expressed in terms of the Caputo time-fractional derivative and a generalized Riemann-Liouville space-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....

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 ...

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...

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. ...

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...

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...

Generalized Fractional Evolution Equation

Da Silva, J. L., Erraoui, M., Ouerdiane, H. (2007)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20 In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does...

Some Fractional Extensions of the Temperature Field Problem in Oil Strata

Boyadjiev, Lyubomir (2007)

Fractional Calculus and Applied Analysis

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This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands...

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,...