{"title":"Solving Hilfer fractional dirac systems: a spectral approach","authors":"Ahu Ercan, Erdal Bas, Ramazan Ozarslan","doi":"10.1007/s00419-025-02767-x","DOIUrl":null,"url":null,"abstract":"<div><p>In this study, we define Hilfer fractional Dirac system. Our main object is to analyze the main spectral structure of the Hilfer fractional Dirac system. To this end, the self-adjointness of the Hilfer fractional Dirac operator, orthogonality of the eigen-vector-functions, and reality of the eigenvalues are displayed. Also, we obtain the representation of the solution of the system by using Laplace transforms with analytical estimations. We investigate eigen-vector functions and eigenvalues for the Hilfer fractional Dirac boundary value problem and illustrate the results in detail with tables and figures.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 2","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00419-025-02767-x.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00419-025-02767-x","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, we define Hilfer fractional Dirac system. Our main object is to analyze the main spectral structure of the Hilfer fractional Dirac system. To this end, the self-adjointness of the Hilfer fractional Dirac operator, orthogonality of the eigen-vector-functions, and reality of the eigenvalues are displayed. Also, we obtain the representation of the solution of the system by using Laplace transforms with analytical estimations. We investigate eigen-vector functions and eigenvalues for the Hilfer fractional Dirac boundary value problem and illustrate the results in detail with tables and figures.
期刊介绍：
Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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