Numerical solution of fractional Fredholm integro-differential equations by spectral method with fractional basis functions

This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical polynomials such as Chebyshev, Legendre, Laguerre, etc, with a low order of convergence. For this reason, the development of classic numerical methods to solve such problems becomes a challenging issue. Since the non-smooth solutions have the same asymptotic behavior with polynomials of fractional powers, therefore, fractional basis functions are the best candidate to overcome the drawbacks of the accuracy of the spectral methods. On the other hand, the fractional integration of the fractional polynomials functions is in the class of fractional polynomials and this is one of the main advantages of using the fractional basis functions. In this paper, an implicit spectral collocation method based on the fractional Chelyshkov basis functions is introduced. The framework of the method is to reduce the problem into a nonlinear system of equations utilizing the spectral collocation method along with the fractional operational integration matrix. The obtained algebraic system is solved using Newton's iterative method. Convergence analysis of the method is studied. The numerical examples show the efficiency of the method on the problems with smooth and non-smooth solutions in comparison with other existing methods

Numerical Solution of Fractional Order Fredholm Integro-differential Equations by Spectral Method with Fractional Basis Functions

This paper introduces a new numerical technique based on the implicit spectral collocation method and the fractional Chelyshkov basis functions for solving the fractional Fredholm integro-differential equations. The framework of the proposed method is to reduce the problem into a nonlinear system of equations utilizing the spectral collocation method along with the fractional operational integration matrix. The obtained algebraic system is solved using Newton’s iterative method. Convergence analysis of the method is studied. The numerical examples show the efficiency of the method on the problems with non-smooth solutions

Heat and mass transfer analysis of radiative and chemical reactive effects on MHD nanofluid over an infinite moving vertical plate

A comparative study of nanofluid (Cu–H2O) and pure fluid (water) is investigated over a moving upright plate surrounded by a porous surface. The novelty of the study includes the unsteady laminar MHD natural transmission flow of an incompressible fluid, to get thermal conductivity of nanofluid is more than pure fluid. The chemical reaction of this nanofluid with respect to radiation absorption is observed by considering the nanoparticles to attain thermal equilibrium. The present work is validated with the previously published work. The upright plate travels with a constant velocity u0, and the temperature and concentration are considered to be period harmonically independent with a constant mean at the plate. The most excellent appropriate solution to the oscillatory pattern of boundary layer equations for the governing flow is computed utilizing the Perturbation Technique. The impacts of factors on velocity, temperature, and concentration are visually depicted and thoroughly elucidated. The fluid features in the boundary layer regime are explored visually and qualitatively. This enhancement is notably significant for copper nanoparticles.The work of U.F.-G. was supported by the government of the Basque Country for the ELKARTEK21/10 KK-2021/00014 and ELKARTEK20/78 KK-2020/00114 research programs

Performance of magnetic dipole contribution on ferromagnetic non-Newtonian radiative MHD blood flow: An application of biotechnology and medical sciences

Casson flow ferromagnetic liquid blood flow over stretching region is studied numerically. The domain is influence by radiation and blood flow velocity and thermal slip conditions. Blood acts an impenetrable magneto-dynamic liquid yields governing equations. The conservative governing nonlinear partial differential equations, reduced to ODEs by the help of similarity translation technique. The transport equations were transformed into first order ODEs and the resultant system are solved with help of 4th order R-K scheme. Performing a magnetic dipole with a Casson flow across a stretched region with Brownian motion and Thermophoresis is novelty of the problem. Significant applications of the study in some spheres are metallurgy, extrusion of polymers, production in papers and rubber manufactured sheets. Electronics, analytical instruments, medicine, friction reduction, angular momentum shift, heat transmission, etc. are only few of the many uses for ferromagnetic fluids. As ferromagnetic interaction parameter value improves, the skin-friction, Sherwood and Nusselt numbers depreciates. A comparative study of the present numerical scheme for specific situations reveals a splendid correlation with earlier published work. A change in blood flow velocity magnitude has been noted due to Casson parameter. Increasing change in blood flow temperature noted due to Casson parameter. Skin-friction strengthened and Nusselt number is declined with Casson parameter. The limitation of current work is a non-invasive magnetic blood flow collection system using commercially available magnetic sensors instead of SQUID or electrodes.Unai Fernandez-Gamiz was supported by Government of the Basque Country [ELKARTEK21/10KK-2021/00014 & ELKARTEK22/85]. Irfan Nurhidayat was supported by King Mongkut’s Institute of Technology Ladkrabang (KMITL), Bangkok, Thailand [KDS2020/045]

Property Aˉ \bar{A} of third-order noncanonical functional differential equations with positive and negative terms

In this article, we have derived a new method to study the oscillatory and asymptotic properties for third-order noncanonical functional differential equations with both positive and negative terms of the form \begin{equation*} (p_2 (t)(p_1 (t) x'(t) )')'+a(t)g(x(\tau(t)))-b(t)h(x(\sigma(t)) = 0 \end{equation*} Firstly, we have converted the above equation of noncanonical type into the canonical type using the strongly noncanonical operator and obtained some new conditions for Property $\bar{A}$. We furnished illustrative examples to validate our main result

A Fuzzy Method for Solving Fuzzy Fractional Differential Equations Based on the Generalized Fuzzy Taylor Expansion

In this field of research, in order to solve fuzzy fractional differential equations, they are normally transformed to their corresponding crisp problems. This transformation is called the embedding method. The aim of this paper is to present a new direct method to solve the fuzzy fractional differential equations using fuzzy calculations and without this transformation. In this work, the fuzzy generalized Taylor expansion by using the sense of fuzzy Caputo fractional derivative for fuzzy-valued functions is presented. For solving fuzzy fractional differential equations, the fuzzy generalized Euler’s method is introduced and applied. In order to show the accuracy and efficiency of the presented method, the local and global truncation errors are determined. Moreover, the consistency, convergence, and stability of the generalized Euler’s method are proved in detail. Eventually, the numerical examples, especially in the switching point case, show the flexibility and the capability of the presented methodThe work of J.J. Nieto has been partially supported by Agencia Estatal de Investigación (AEI) of Spain under grant MTM2016-75140-P, co-financed by the European Community fund FEDER, and XUNTA de Galicia under grants GRC2015-004 and ED431C 2019/02S

A chemical engineering application on hyperbolic tangent flow examination about sphere with Brownian motion and thermo phoresis effects using BVP5C

Brownian motion and thermophoresis impacts are discussed in relation to a tangent hyperbolic fluid encircling a sphere subject to a convective boundary condition and a Biot number. Concentration boundary conditions involving a wall normal flow of zero nanoparticles are an unexplored area of research. The governing non-linear BVP is transformed into a higher-order non-linear ODE using similarity transformations. Following equations were numerically solved for various values of emerging parameters using the matlab function bvp5c. Calculated values for velocity, concentration, temperature, the skin friction coefficient, Sherwood and Nusselt numbers are all shown, tabulated for analysis. Laminar boundary layer flow and heat transfer from a sphere in two-dimensional nano fluid is the novelty of the current work. The Weissenberg number decreases the velocity boundary layer thickness. The Biot number parameter lowers the field's temperature and speed

Computational analysis of bio-convective eyring-powell nanofluid flow with magneto-hydrodynamic effects over an isothermal cone surface with convective boundary condition

Non-Newtonian fluids are essential in situations where heat and mass transfer are involved. Heat and mass transfer processes increase efficiency when nanoparticles (0.01≤φ≤0.03) are added to these fluids. The present study implements a computational approach to investigate the behavior of non-Newtonian nanofluids on the surface of an upright cone. Viscous dissipation (0.3≤Ec≤0.9) and magnetohydrodynamics (MHD) (1≤M≤3) are also taken into account. Furthermore, we explore how microorganisms impact the fluid's mass and heat transfer. The physical model's governing equations are transformed into ordinary differential equations (ODEs) using a similarity transformation to make the analysis easier. The ODEs are solved numerically using the Bvp4c solver in MATLAB. The momentum, thermal, concentration, and microbe diffusion profiles are graphically represented in the current research. MHD (1≤M≤3) effects improve the diffusion of microbes, resulting in increased heat and mass transfer rates of 18 % and 19 %, respectively, based on our results. Furthermore, a comparison of our findings with existing literature demonstrates promising agreement

Free convection flow from a heated cone with a downward tip submerged in Newtonian fluids employing a finite volume technique

Computational fluid dynamics technique have been employed to capture the plain convective flow past from a heated cone with a tip downward in various stagnant Newtonian fluids. Using detailed isotherm patterns around the cone under steady-state conditions examine the heat transfer characteristics that have been reported. The findings illustrate the distribution of the friction factor, average Nusselt number and local Nusselt number around the cone surface over a wide range of dimensionless values such as Grashof and Prandtl numbers. The guiding PDEs such as conservation of mass, momentum and energy are solved by finite volume method using commercial software of ANSYSCFX16.0. To simplify the governing equations while capturing the natural convection, Boussinesq approximation has been adopted to coupling the flow and temperature fields.This study reveals the contribution of various angles (φ = 15°,300and45°), diverse Prandtl numbers (Pr = 0.71,5,10,20,50) and distinct Grashof numbers (GrL = 104, 105, 106) for the efficacy of them over the slant surface of the cone. The heat transmission and parametric features of these processes have been discussed for how heat can be transferred from a heated cone when it is submerged in a liquid. Visualization of the effects of different parameters for different cone apex angles was done by displaying the results graphically. The present simulations are in a near match to the numeric values appeared in the literature