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dc.contributor.authorEl-Amin, Mohamed F.
dc.date.accessioned2024-05-26T05:51:50Z
dc.date.available2024-05-26T05:51:50Z
dc.date.issued2024-07-31
dc.identifier.urihttp://hdl.handle.net/20.500.14131/1691
dc.description.abstractThis chapter introduces the analytical solutions of fractional partial differential equations (PDEs), focusing on their significance in modeling transport phenomena that exhibit anomalous diffusion or non-local dynamics. The chapter begins by exploring power-series methods for solving fractional differential equations (FDEs), illustrating the technique through examples such as gas flow in porous media and boundary-layer flow. It then transitions to the Adomian Decomposition Method (ADM), a semi-analytical approach that simplifies the solution of nonlinear, fractional-order differential equations. Through detailed examples, including the time-fractional convection-conduction equation, the time-fractional diffusion-reaction equation, time and time-space fractional advection-diffusion equation, the chapter showcases the versatility and efficiency of ADM in handling complex fractional PDEs. Finally, the diffusion equation with time Caputo-Fabrizio fractional derivative has been solved using Laplace transform method.en_US
dc.publisherElseiveren_US
dc.subjectFractional Differential Equations, Power-Series Solutions, Adomian Decomposition Method (ADM), Gas Flow in Porous Media, Boundary-Layer Flow, Convection-Conduction Equation, Diffusion-Reaction Equation, Laplace transform method, Hyper-geometric functionen_US
dc.titleChapter 4: Analytical Solutions of Fractional PDEs, in the Book: Fractional Modelling of Fluid Flow and Transport Phenomenaen_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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