Unbounded solutions to abstract boundary value problems of fractional differential equations on a half line

Wang, Fuli; Cui, Yujun

doi:10.1002/mma.5819

Math Methods in App Sciences

2019

DOI: 10.1002/mma.5819

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Unbounded solutions to abstract boundary value problems of fractional differential equations on a half line

Fuli Wang

Yujun Cui

Abstract: In this paper, we investigate the existence of solutions to abstract boundary value problems of fractional differential equations on . The choice of the Banach space allows the solutions to be unbounded. Our approach mainly depends on the technique of Hausdorff measure of noncompactness in conjunction with the criterion of compactness in . Finally, an example in the Banach sequence space ℓ1 is given to illustrate our results.

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“…The existence of solutions to abstract boundary value problems of fractional differential equations is investigated in Wang and Cui. 21 The Banach sequence space is applied for illustration of the obtained results. Tian et al 22 have proposed interesting analysis for a theoretical model of dust ion-acoustic waves in collisionless and unmagnetized dust plasma.…”

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Preface to a thematic special issue of methods of mathematics and fractional calculus

Zeidan

Herbst

2021

Math Methods in App Sciences

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Preface to a thematic special issue of methods of mathematics and fractional calculus Mathematics is a common and widespread language that is not spoken very well in different parts of the world. This language also occurs in diverse forms that are required in different methods and applications. Today, mathematics is used everywhere from sciences and engineering to foreign languages research and the frontiers of social sciences. The key objective of this thematic special issue has been to offer typical attention on the latest advances and trends in different methods of mathematics and fractional calculus. Given the increasingly wide branches of mathematics, it is impossible to encapsulate a thorough representation of the selected topics in a single journal issue. However, it is possible to proffer a thematic special issue to bring together diverse fields of mathematics as well as a range of researchers from different parts of the world to represent a valued panel that addresses the different aspects and methods of mathematics, from pure, applied mathematics to fractional calculus.Manuscripts in this thematic special issue were requested through a general call and by invitation. It also includes selected papers that were presented at the International Conference on Fractional Differentiation and its Applications-ICFDA'18 held in Amman, Jordan, on July 16-18, 2018. All submissions were subject to a rigorous peer-review process following the well-known policies and standards of the Mathematical Methods in the Applied Sciences journal. Every submission was reviewed by at least two internationally established experts in the topic of that paper. The total number of papers received in response to the call of this thematic special issue was 90. Forty-nine papers were rejected after the peer-review process, and 41 were accepted upon up to three revisions and after an agreement was reached by the referees and the editors. Therefore, the rejection rate for this issue is 54.45%, which is one of the indicators of the high standards and quality considered when preparing this thematic special issue.In the following, we give a sense of the 41 accepted papers and the diversity of this thematic special issue where all papers are listed in references by their authors, title and DOI. The first paper by Dassios and Baleanu 1 investigates a class of singular linear systems of fractional differential equations with given inconsistent initial conditions. Validation of the proposed theory and analysis were carried out through numerical examples. Boumenir and Tuan 2 show that it is possible to uniquely recover the coefficient of an one-dimensional fractional diffusion equation from a single boundary measurement. An algorithm based on the well-known Gelfand-Levitan inverse spectral theory of Sturm-Liouville operators was developed and validated. The paper by Senol et al 3 deals with numerical methods for a KdV-like model. It was shown that the developed methods for the model equations are user-friendly and can be easily implemented to other...

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confidence: 99%

Preface to a thematic special issue of methods of mathematics and fractional calculus

Zeidan

Herbst

2021

Math Methods in App Sciences

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On implicit impulsive Langevin equation involving mixed order derivatives

Zada

Rizwan

et al. 2019

Adv Differ Equ

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Positive Solutions for a System of Fractional Integral Boundary Value Problems of Riemann–Liouville Type Involving Semipositone Nonlinearities

Ding

2019

Mathematics

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In this work by the index of fixed point and matrix theory, we discuss the positive solutions for the system of Riemann–Liouville type fractional boundary value problems D 0 + α u ( t ) + f 1 ( t , u ( t ) , v ( t ) , w ( t ) ) = 0 , t ∈ ( 0 , 1 ) , D 0 + α v ( t ) + f 2 ( t , u ( t ) , v ( t ) , w ( t ) ) = 0 , t ∈ ( 0 , 1 ) , D 0 + α w ( t ) + f 3 ( t , u ( t ) , v ( t ) , w ( t ) ) = 0 , t ∈ ( 0 , 1 ) , u ( 0 ) = u ′ ( 0 ) = ⋯ = u ( n − 2 ) ( 0 ) = 0 , D 0 + p u ( t ) | t = 1 = ∫ 0 1 h ( t ) D 0 + q u ( t ) d t , v ( 0 ) = v ′ ( 0 ) = ⋯ = v ( n − 2 ) ( 0 ) = 0 , D 0 + p v ( t ) | t = 1 = ∫ 0 1 h ( t ) D 0 + q v ( t ) d t , w ( 0 ) = w ′ ( 0 ) = ⋯ = w ( n − 2 ) ( 0 ) = 0 , D 0 + p w ( t ) | t = 1 = ∫ 0 1 h ( t ) D 0 + q w ( t ) d t , where α ∈ ( n − 1 , n ] with n ∈ N , n ≥ 3 , p , q ∈ R with p ∈ [ 1 , n − 2 ] , q ∈ [ 0 , p ] , D 0 + α is the α order Riemann–Liouville type fractional derivative, and f i ( i = 1 , 2 , 3 ) ∈ C ( [ 0 , 1 ] × R + × R + × R + , R ) are semipositone nonlinearities.

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Unbounded solutions to abstract boundary value problems of fractional differential equations on a half line

Cited by 4 publications

References 8 publications

Preface to a thematic special issue of methods of mathematics and fractional calculus

Preface to a thematic special issue of methods of mathematics and fractional calculus

On implicit impulsive Langevin equation involving mixed order derivatives

Positive Solutions for a System of Fractional Integral Boundary Value Problems of Riemann–Liouville Type Involving Semipositone Nonlinearities

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