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Analysis for advection–diffusion problem subject to memory effects and local and nonlocal kernels: A fractional operators approach

Qasim AliDepartment of Mathematics, University of Engineering and Technology, Lahore, PakistanKamel Al‐KhaledDepartment of Mathematics & Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, JordanJiyan OmarAli RazaDepartment of Mathematics, University of Engineering and Technology, Lahore, PakistanSami Ullah KhanDepartment of Mathematics, COMSATS University Islamabad, Sahiwal 57000, PakistanM. Ijaz KhanDepartment of Mechanical Engineering, Lebanese American University, P. O. Box 36, Beirut, LebanonS.A. NajatiDepartment of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaMowffaq OreijahMechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, P.O. Box 5555, Makkah 21955, Saudi ArabiaKamel GuedriResearch Unity: Materials, Energy and Renewable Energies, Faculty of Science of Gafsa University of Gafsa, Gafsa 2100, TunisiAhmed M. GalalProduction Engineering and Mechanical Design Department, Faculty of Engineering Mansoura University, P.O. 35516, Mansoura, Egypt

2022en

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Annotatsiya

In this communication, a familiar physical phenomenon along with a time-dependent concentration source in a one-dimensional fractional differential advection–diffusion has been worked out. The problem is supported with the boundary with initial and boundary conditions. First of all, the results for the nondimensional classical advection–diffusion process are deliberated utilizing the Laplace coupled with finite sine-Fourier transforms analytically. Later on, the analysis is expanded for different fractional operators. The inspection of memory factors is presented through Mathcad. The impacts of the fractional (memory) parameter upon the solute concentration are discussed by making use of Mathcad15. A detailed physical significance of the fractional problem in view of the parameters is studied. It is noted that the decreasing change in concentration is associated with the larger values of noninteger parameter.

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DOI: 10.1142/s0217979223500996

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