Volume-11 , Issue-5 , Oct 2024, ISSN 2348-4519 (Online)

• Open Access   Article

  On the Presence of Positive Solutions for Generalized Fractional Boundary Value Problems with Green’s Function

  Ibrahim A. Al-Mania

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.5 , pp.1-10, Oct-2024

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  Abstract
  The branch of mathematics that deals with the study of non-integer order derivatives and integrals is called fractional calculus. The interesting thing about this subject is that in contrast to the classical derivatives, the fractional derivatives are not a point quantity. Indeed, the fractional derivative of a function of order ? at some point is a local property only for ? being an integer. In recent years, the study of positive solutions for fractional differential equation boundary value problems has attracted considerable attention, and fruits from research into it emerge continuously. In this paper, the existence of positive solutions is established for boundary value problems defined within generalized Riemann–Louville and Caputo fractional operators. Our approach is based on utilizing the technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green’s function and study their properties for three different types of boundary value problems. An example is presented to demonstrate the validity of theoretical findings.

  Key-Words / Index Term
  Existence of positive solutions; Fractional Calculus; Riemann-Liouville Differintegral; Generalized Fractional Boundary Value Problems

  References
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  [15] Jeelani, M. B., Saeed, A. M., Abdo, M. S., & Shah, K. “Positive solutions for fractional boundary value problems under a generalized fractional operator”. Mathematical Methods in the Applied Sciences, 44.11: pp.9524-9540, 2021.?
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  Citation
  Ibrahim A. Al-Mania, "On the Presence of Positive Solutions for Generalized Fractional Boundary Value Problems with Green’s Function," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.5, pp.1-10, 2024

• Open Access   Article

  Numerical Simulation for an Electron Magnetohydrodynamic (EMHD) Nanofluid with Iron Oxide (Fe3O4) under the triple effects of an Electric field, Heat generation/Absorption and Impermeability of the Surface

  A.G. Madaki, A.A. Hussaini, R. Roslan, A.B. Umar

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.5 , pp.11-22, Oct-2024

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  Abstract
  our exploration is mainly concerned with the heat transfer properties of Fe3O4 -water base nanofluid past on an exponential impermeable shrinking/stretching surface. We examined how a boundary layer fluid flow toward a shrinking/stretching surface is affected by the combined actions of an electric field, heat generation/absorption and surface impermeability. Partial differential equations (PDEs) are used to illustrate the flow sensation. Making use of the proper similarity transformation technique, the system of ODEs is derived from the PDEs. The shooting method is then applied to these updated equations. According to the analysis, the Momentum profile is amplified with an increase in heat generation/ absorption, variable viscosity and magnetic field. The reverse is the case with an increased impermeability parameter. Furthermore, the temperature profile is enhanced with an increase in impermeability and electricity. The results may find use in a variety of technical domains, including the optimization of petroleum pipeline flow. The findings can direct further research in this field and advance our understanding of heat and mass transfer phenomena.

  Key-Words / Index Term
  Heat generation/ absorption, Electric field, Suction/ injection, Magnetic field, Nanofluid

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  Citation
  A.G. Madaki, A.A. Hussaini, R. Roslan, A.B. Umar, "Numerical Simulation for an Electron Magnetohydrodynamic (EMHD) Nanofluid with Iron Oxide (Fe3O4) under the triple effects of an Electric field, Heat generation/Absorption and Impermeability of the Surface," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.5, pp.11-22, 2024