Inverse Problems for Degenerate Fractional Integro-Differential Equations

Horani, Mohammed Al; Fabrizio, Mauro; Favini, Angelo; Tanabe, Hiroki

doi:10.3390/math8040532

Cited by 3 publications

(4 citation statements)

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“…This problem is called degenerate, if the operator B is not invertible. Recently, these types of fractional abstract Cauchy problems have been studied using different methods, see [2,3]. Moreover, similar results where the derivative is the classical one can be found in [22,23].…”

Section: Introductionmentioning

confidence: 76%

“…, }. Let A : Dom(A) ⊆ 2 → 2 be a densely defined closed linear operator on 2 , where domain of A contains the elements of the natural basis of 2 .…”

Section: Resultsmentioning

confidence: 99%

“….} is the natural basis of 2 . The derivative in the above problem is the conformable derivative, precisely: for f : [0; ∞) → R and 0 < α 1, the conformable fractional derivative of f of order α is defined by…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Infinite rank solution for conformable degenerate abstract Cauchy problem in Hilbert spaces

Seddiki¹,

Horani²,

Khalil³

2023

J. Math. Computer Sci.

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Section: Introductionmentioning

confidence: 76%

“…, }. Let A : Dom(A) ⊆ 2 → 2 be a densely defined closed linear operator on 2 , where domain of A contains the elements of the natural basis of 2 .…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Infinite rank solution for conformable degenerate abstract Cauchy problem in Hilbert spaces

Seddiki¹,

Horani²,

Khalil³

2023

J. Math. Computer Sci.

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“…For Riemann-Liouville derivative Dα t of orderα, we address the monograph [11] (see also [12,13]). Very recent applications concerning Caputo fractional derivative operator are also discussed in [14] by the same authors using a completely different method than Sviridyuk's group (see [15,16]). Some related topics can be found in [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Fractional Cauchy Problems for Infinite Interval Case-II

et al. 2019

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We consider fractional abstract Cauchy problems on infinite intervals. A fractional abstract Cauchy problem for possibly degenerate equations in Banach spaces is considered. This form of degeneration may be strong and some convenient assumptions about the involved operators are required to handle the direct problem. Required conditions on spaces are also given, guaranteeing the existence and uniqueness of solutions. The fractional powers of the involved operator B X have been investigated in the space which consists of continuous functions u on [ 0 , ∞ ) without assuming u ( 0 ) = 0 . This enables us to refine some previous results and obtain the required abstract results when the operator B X is not necessarily densely defined.

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Elaboration of an Algorithm for Solving Hierarchical Inverse Problems in Applied Economics

Gribanova

2022

Mathematics

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One of the key tools in an organization’s performance management is the goal tree, which is used for solving both direct and inverse problems. This research deals with goal setting based on a model of the future by presenting the goal and subgoal in the form of concrete quantitative and qualitative characteristics and stepwise formation of factors. A stepwise solution to a factor generation problem is considered on the basis of mathematical symmetry. This paper displays an algorithm for solving hierarchical inverse problems with constraints, which is based on recursively traversing the vertices that constitute the separate characteristics. Iterative methods, modified for the case of nonlinear models and the calculation of constraints, were used to generate solutions to the subproblems. To realize the algorithm, the object-oriented architecture, which simplifies the creation and modification of software, was elaborated. Computational experiments with five types of models were conducted, and the solution to a problem related to fast-food restaurant profit generation was reviewed. The metrics of remoteness from set values and t-statistics were calculated for the purpose of testing the received results, and solutions to the subproblems, with the help of a mathematical package using optimization models and a method of inverse calculations, were also provided. The results of computational experiments speak to the compliance of the received results with set constraints and the solution of separate subproblems with the usage of the mathematical package. The cases with the highest solution accuracy reached are specified.

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Inverse Problems for Degenerate Fractional Integro-Differential Equations

Cited by 3 publications

References 20 publications

Infinite rank solution for conformable degenerate abstract Cauchy problem in Hilbert spaces

Infinite rank solution for conformable degenerate abstract Cauchy problem in Hilbert spaces

Fractional Cauchy Problems for Infinite Interval Case-II

Elaboration of an Algorithm for Solving Hierarchical Inverse Problems in Applied Economics

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