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dc.contributor.authorEl-Amin, Mohamed F.
dc.date.accessioned2024-05-26T05:49:46Z
dc.date.available2024-05-26T05:49:46Z
dc.date.issued2024-07
dc.identifier.urihttp://hdl.handle.net/20.500.14131/1688
dc.description.abstractThis chapter presents the concepts of fractional calculus used in the field of fluid mechanics required in the rest of the book. The chapter begins with an overview and then introduces preliminary concepts crucial for understanding fractional calculus, including the Gamma and Beta functions, the Mittag-Leffler function, and various fractional operators. These foundational elements are essential for grasping the more complex aspects of fractional calculus in fluid mechanics. Moreover, the chapter examines different fractional derivative models, providing the basic definition of several key types. These include the Riemann-Liouville, Caputo, Grünwald-Letnikov, Caputo-Fabrizio, and Atangana-Baleanu fractional derivatives. Each model is explored, offering insights into their unique characteristics and applications. Also, a significant portion of the chapter is dedicated to the Laplace transform, which covers its definition, basic principles, and properties, along with a list of common Laplace transforms and techniques for applying the inverse Laplace transform. This comprehensive coverage equips readers with the tools to use the Laplace transform in various contexts of fractional calculus. The chapter ends with exercises designed to reinforce the concepts covered.en_US
dc.publisherElseiveren_US
dc.subjectGamma Functio, Beta Function, Mittag-Leffler Function, Fractional Operators, Riemann-Liouville Fractional Derivative, Caputo Fractional Derivative, Grünwald-Letnikov Fractional Derivative, Caputo-Fabrizio Fractional Derivative, Atangana–Baleanu Fractional Derivative, Laplace Transform, Inverse Laplace Transformen_US
dc.titleChapter 2: Fundamentals of Fractional Calculusen_US
dc.source.booktitleFractional Modelling of Fluid Flow and Transport Phenomenaen_US
dc.contributor.researcherNo Collaborationen_US
dc.contributor.labEnergy Laben_US
dc.subject.KSAMTHen_US
dc.contributor.ugstudent0en_US
dc.contributor.alumnae0en_US
dc.source.indexScopusen_US
dc.contributor.departmentNSMTUen_US
dc.contributor.pgstudent0en_US
dc.contributor.firstauthorEl-Amin, Mohamed F.


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