Rothe time discretization method for fractional integro-differential equations

Bahuguna, D.; Jaiswal, Anjali

doi:10.1080/15502287.2019.1600075

Cited by 5 publications

(4 citation statements)

References 15 publications

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“…Lemma 2.4. [4] Suppose that the function η(t) ≥ 0 is continuous or piecewise continuous on 0 < t ≤ T and ξ (t) be positive continuous function on 0 ≤ t ≤ T . If M and 0 < α < 1 are such that…”

Section: Assumptions and Preliminariesmentioning

confidence: 99%

“…Lemma 3.7. ( [4]) There exists a subsequence {Y n k } of {Y n } such that d − Y n k dt dy dt and D α 0+…”

Section: Discretization Scheme and A Priori Estimatesmentioning

confidence: 99%

“…Many researchers adopted this method for solving various type of differential equations. The role of Rothe's method in the study of integer order and fractional order differential equations has been seen in various papers (see- [5], [3], [15], [4], [14], [16], [30]). This method has been well-founded as an efficient tool in solving partial differential equations and gives a numerical approach to find approximate solution.…”

Section: Introductionmentioning

confidence: 99%

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Application of Rothe’s method to fractional differential equations

Bahuguna¹,

Jaiswal²

2019

Malaya J. Mat.

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In this paper we consider an initial value problem for a fractional differential equation formulated in a Banach space X where the fractional derivative is Riemann-Liouville type of order 0 < α < 1. We establish the existence and uniqueness of a strong solution of the problem by applying the method of semi-discretization in time, also known as the method of lines or more popularly as Rothe's method. The dual space X * of X is assumed to be uniformly convex. In the final section, we illustrate the applicability of the theoretical results with the help of an example.

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Section: Assumptions and Preliminariesmentioning

confidence: 99%

“…Lemma 3.7. ( [4]) There exists a subsequence {Y n k } of {Y n } such that d − Y n k dt dy dt and D α 0+…”

Section: Discretization Scheme and A Priori Estimatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of Rothe’s method to fractional differential equations

Bahuguna¹,

Jaiswal²

2019

Malaya J. Mat.

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“…The existence, uniqueness and regularity of a strong solution are provided utilizing Rothe's method. Second, a fractional-order partial integrodifferential equation with initial/boundary conditions has been studied in [31]. Rothe's method was used to prove the existence and uniqueness of a strong solution to the integrodifferential equation, which ensures that the initial boundary value problem is well-posed.…”

Section: Introductionmentioning

confidence: 99%

Space-dependent variable-order time-fractional wave equation: Existence and uniqueness of its weak solution

Bockstal

Hendy

Zaky

2022

Quaestiones Mathematicae

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The investigation of an initial-boundary value problem for a fractional wave equation with space-dependent variableorder wherein the coefficients have a dependency on the spatial and time variables is the concern of this work. This type of variable-order fractional differential operator originates in the modelling of viscoelastic materials. The global in time existence of a unique weak solution to the model problem has been proved under appropriate conditions on the data. Rothe's time discretization method is applied to achieve that purpose.

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