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Abstract: Abstract The present work aims to investigate the approximate solution to a general form of higher-order boundary value problem of both linear and nonlinear types. A novel Genocchi polynomial-based method is adapted for solving the model through a matrix collocation-based method. The considered model is investigated using the presented technique which mainly converts the equation into a system of algebraic equations. This system is then solved using a new algorithm. The method is tested on several examples and the acquired results prove that the method is accurate compared to other techniques from the literature. The method is straightforward and fast in terms of computational effort and is considered a promising technique for solving similar problems. PubDate: 2022-05-24
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Abstract: Abstract This work concerned with the oblique traveling wave solutions of coupled space-time fractional (2 + 1)-dimensional dispersive long wave equations (DLWE) for understanding the basic features of resonance wave dynamics in science and engineering, mainly in water wave dynamics. The generalized exp(− \({\Psi }\) (ζ))-expansion scheme mutually by means of conformable derivatives is implemented to seek several types of faithful solutions of coupled DLWE. The oblique traveling wave solutions are displayed in the forms of trigonometric, hyperbolic and rational functions through physical and some supplementary free parameters. It is predicted that the obliqueness is significantly modified the oppositely propagating long waves assuming the suitable values of the parameters. PubDate: 2022-05-24
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Abstract: Abstract Cancer is one of the biggest threats around the globe, albeit medical action has been prosperous, despite large challenges, at least for some diagnostics. A magnificent effort of personal and financial resources is dedicated, with flourishing results(but also with failures), to cancer analysis with special consideration to experimental and analytical immunology. Fractal-fractional operators have manifested the enigmatic performance of numerous natural phenoms, which ordinarily do not foretell in ordinary ones and fractional operators. In this study, we examine an Immune-Tumor dynamical system supporting the fractal-fractional frame. We authenticate the existence theory to guarantee the suggested system maintains at least one answer through Schauder’s fixed point theorem. Additionally, Banach’s fixed theory affirms the uniqueness of the answer to the aimed problem. A Non-linear functional examination was carried out to affirm that the introduced system is stable with respect to Ulam-Hyres’s theory supporting the fractal-fractional operator. Behavior of the offered problem is presented through the graphical representations, for the different amounts of fractional order and fractal orders successfully. PubDate: 2022-05-20
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Abstract: Abstract The dynamical behavior of chaotic processes with a noninteger-order operator is considered in this work. A lot of scientific reports have justified that modeling of physical scenarios via non-integer order derivatives is more reliable and accurate than integer-order cases. Motivated by this fact, the standard time derivatives in the model equations are formulated with the novel Caputo fractional-order operator. The choice of using the Caputo derivative among several existing fractional derivatives has to do with the fact that it gives way for both the initial conditions and boundary conditions to be incorporated in the development of the chaotic model. Numerical approximation of fractional derivatives has been the major challenge of many scholars in different areas of engineering and applied sciences. Hence, we developed a numerical approximation technique, which is based on the Chebyshev spectral method for solving the integer-order and non-integer-order chaotic systems which are largely found in physics, finance, biology, engineering, and other areas of applied sciences. The proposed numerical method used here is easy to implement on a digital computer, and capable of solving higher-order problems without reduction to the system of lower-order ordinary differential equations with limited computational costs. Experimental results are presented for different instances of fractional-order parameters. PubDate: 2022-05-19
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Abstract: Abstract The key objective of the paper is to extend the Bessel wavelet transform and fractional Bessel wavelet transform to distributions of slow growth using adjoint method. We prove the continuity of Bessel wavelet transform and its inverse in a suitable Zemanian type space. Based on this, the continuity of fractional Bessel wavelet transform and its inverse is proved in the above space. Using the continuity results, these transforms are extended as an adjoint to the corresponding dual space of distributions. The examples of Bessel wavelet transform of a polynomial function and a distribution are given. The Schrödinger equation is solved using the Bessel wavelet transform. PubDate: 2022-05-18
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Abstract: Abstract From the current scenario it is well known that the most of the engineering problem leads to the mathematical model with different concept. Associated with these phenomena, the present investigation gathers some physical interpretation of different model that leads to couple nonlinear time fractional differential equation encompass with variable order within certain domain relating to the physical significance of the corresponding problem. The system of equations is based upon Caputo-type fractional differential equation in particular cases. The crux of this investigation is that the use of various solution approach for the modeled problems such as “Reduced Differential Transform Method” and “Adomian Decomposition Method”. Finally, the aforesaid methodologies are also applicable for the infectious diseases model and verified in particular case of integral order with an earlier investigation. PubDate: 2022-05-17
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Abstract: Abstract The solitary wave solutions gained well-reputed significance because of their peculiar characteristics. Solitary waves are spatially localized waves and are found in a variety of natural systems from mathematical physics and engineering phenomena. This manuscript deals the investigation of optical pulses to the Biswas–Arshed equation with third order dispersion and self-steepening coefficients in nonlinear optics. Various optical pulses are recovered in single and combo shapes like bright, dark, singular, bright-dark, and dark-singular solitons by the virtue of extended sinh-Gordon equation expansion method and ( \(\frac{G^{\prime }}{G^2}\) )-expansion function method. Besides, the singular periodic wave solutions are also derived. The constraints conditions to ensure the existence criteria of reported optical solutions are also listed. In addition, by selecting different parametric values, the physical representation of some achieved solutions is plotted in 3D graphs with the help of Mathematica. The reported results show that the proposed methods are effective, concise, straightforward, powerful, and they can be used to tackle some more complex nonlinear systems. PubDate: 2022-05-17
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Abstract: Abstract This study analyses the rheological characteristics of non-Newtonian Carreau fluid model for nanoparticles suspended flow of blood through constricted arteries in the presence of stenosis, thrombosis and catheters. Analytical expressions, such as, velocity distribution, temperature, pressure gradient, wall shear stress and resistive impedance to flow are obtained by implementing the perturbation method and through the extensive use of MATLAB and MATHEMATICA programming tools, the results are presented graphically and tabularly. It is found that temperature of the fluid lessens with the increase in stenosis shape parameter and depth of stenosis which results in the reduction of flow of blood in the artery. It is discovered that a rise in Weissenberg number results in the decrease of fluid’s velocity and skin friction. The magnitude of resistance to blood flow reduces with the upsurge of flow rate and stenosis shape parameter and the reverse character is recognized when Weissenberg number, the depth and axial displacement of blood clot increases. When the angioplasty catheter of radius 0.3 is inserted to the clear the constrictions in the artery, the resistance to flow surges considerably in the range of 6.75–8.78 when the stenosis position extends in the axial direction from 0.1 to 0.3. It is also recorded that when the catheter guidewire radius is 0.18, the pressure gradient in blood flow is found to vary in the range of 1.21–1.43 when the axial variable z varies from 0.2 to 0.8 and it decreases from 1.36 to 1.32 when the blood clot position displaces from 0.2 to 0.6. PubDate: 2022-05-16
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Abstract: Abstract The key aim of the present work is to develop extended fractional calculus results associated with product of the generalized extended Mittag–Leffler function, S-function, general class of polynomials and \({\overline{\text{H}}}\) -function. Some special cases involving various simpler and useful special functions are given to show the importance and utilizations of our main findings. The outcomes are very general in characteristic and can be utilized to derive numerous interesting fractional integral operators involving simpler special functions and polynomials having uses in scientific and engineering problems. PubDate: 2022-05-14
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Abstract: Abstract This study aims to investigate the heat transfer and magnetohydrodynamics flow of fractional Oldroyd-B nanofluid in a porous medium with radiation effect. The Caputo time-fractional derivative model is introduced to develop the Oldroyd-B fluid’s constitutive relationship, which describes both memory and elastic effects. Two kinds of carbon nanotubes, particularly single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with base fluid water are considered for the study. The presence of carbon nanotubes with fractional derivatives made the results advantageous for handling similar heat-regulating industrial and engineering problems like achieving heat transfer management in automobile engines, boiler, heat exchangers, grinders and refrigerators. Nonlinear coupled governing equations involving Caputo time-fractional derivatives are reduced to dimensionless form using suitable non-dimensional quantities. The obtained nonlinear governing equations are solved using finite difference approximation with the combined L1 algorithm. Influence of involved parameters on fluid motion and thermal distribution are presented via plots and discussed in detail. The comparison between two kinds of nanofluids, namely SWCNT Oldroyd-B nanofluid and MWCNT Oldroyd-B nanofluid are studied and noticed that MWCNT Oldroyd-B nanofluid provides higher velocity and lower temperature for all embedded parameters. Also, skin-friction and heat transfer rate are controlled by the flow parameters like relaxation and retardation times, relaxation and retardation fractional derivatives, nanoparticle volume fraction, porosity, Darcy number, magnetic and radiation parameters. Furthermore, it is observed that \(\overline{C_{f}}_{{\mathrm{MWCNT Oldroyd{-}B}\,\mathrm{nanofluid}}} > \overline{C_{f}}_{{\mathrm{SWCNT Oldroyd{-}B}\,\mathrm{nanofluid}}}\) and \(\overline{Nu}_{{\mathrm{SWCNT Oldroyd{-}B}\,\mathrm{nanofluid}}} >\overline{Nu}_{{\mathrm{MWCNT Oldroyd{-}B}\, \mathrm{nanofluid}}}\) . PubDate: 2022-05-13
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Abstract: Abstract The majority of the previous studies analyzed the flow of fluid around the perfect sphere however the slight deformations in the shape of the particle are observed in nature. The motivation of the present work is to investigate the impact of MHD flow on slightly deformed sphere embedded in unbounded porous medium. The stream function for the flow field is calculated in terms of Bessel and Gegenbauer functions. As a boundary conditions, vanishing of normal and tangential component of velocity are applied. The resistance force is evaluated past an impermeable spheroid. As a special case, we consider an electrically conducting fluid motion past a rigid oblate spheroid embedded in a porous medium. Also, the expression for non-dimensional drag and dimensionless shearing stress are computed and its variation with Hartmann number, permeability, and deformation parameters are depicted graphically. The flow patterns of the streamline are represented graphically along the axial direction of the spheroidal particles. A number of specific cases are developed and compared to earlier research, demonstrating that our approach is valid. The results show that the magnetic field increases the resistance on the oblate spheroid. The investigation of the current study may be beneficial in the delivery of medications to the desired location, the medical treatment of tumors, cancer, and others. PubDate: 2022-05-13
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Abstract: Abstract A rotating porous surface characterized by the Darcy–Forchheimer model upon which the Williamson micropolar nanofluid discharge occurs is examined to explore the effects of such flow and heat transferring capacity. The magnetic field is also introduced in this non-Newtonian fluid flow to control the fluid motion. Nanofluid is specified by taking the thermal properties of blood and \(\hbox {Fe}_3\hbox {O}_4\) particles. The mathematical structure of the problem is analyzed by considering assumptions used in fluid flow theories with velocity and thermal slip boundary conditions. The governing mathematical equations are simplified by applying similarity transformation variables. The upshots of the current study are obtained by utilizing the bvp4c solver in MATLAB. The micropolar parameter helps in escalating fluid velocity and Nusselt number and enhancing thermal transmission. The outcomes of solutions are plotted through graphs and tables by varying engrossed parameters, and then the observed changes are discussed and highlighted. PubDate: 2022-05-13
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Abstract: Abstract The present paper investigates the combined impacts of Biot number and Richardson number on Casson fluid stream with radiating porous media on flow, heat and mass transfer with convective boundary conditions. The governing flow equations are reduced into ODE’s by applying similarity equations. Matlab is used to solve the reduced equations numerically. The focus of present paper is to study the effects of various constraint like porous parameter and thermal radiation on Casson mixed convection of Richardson and Biot number on stream, energy and mass transfer. Also, the energy transformation increases with rise in thermal radiation is observed. Tables and graphs are used to identify and analyse the impact of relevant limitations on various flow parameters. PubDate: 2022-05-13
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Abstract: Abstract A mathematical model delineating the control strategies in transference of Covid-19 pandemic is examined through Atangana–Baleanu Caputo type fractional derivatives. The total count of people under observation is classified into Susceptible, Vaccinated, Infected and Protected groups (SVIP). The designed model studies the efficiency of vaccination and personal precautions incorporated qualitatively by every individual via fixed point theorem. Stability of the system has been investigated with spectral characterisation of Ulam Hyer’s kind. Numerical interpolation has been derived by Adam’s semi-analytical technique and we have approximated the solution. We have proved the theoretical analysis through graphical simulations that vaccination and self protective interventions are the significant role to decrease the contagious expansion of the virus among the people in process. PubDate: 2022-05-12
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Abstract: Abstract This manuscript provides an efficient and high-accuracy computational technique for solving fractional Black–Scholes equations (FB–SEs) arising in the financial market. In order to find an accurate solution of the mentioned equations, we use the collocation method through the two-dimensional Fibonacci wavelets (2D-FWs). To carry out the scheme, we firstly present 2D-FWs. Then, Riemann–Liouville pseudo-operational matrix for 1 & 2D-FW are achieved. RL pseudo-operational matrix for 2D-FWs and the collocation technique are employed to reduce the mentioned problem into a system of algebraic equations. Moreover, the convergence of the approximate solution to the exact solution is proven by providing an upper bound of error estimate. To reveal the performance and accuracy of the developed method, some numerical experiments are provided. Moreover, we present a brief bibliometric analysis and scientific trends to quantitatively measure research results on considered equations. PubDate: 2022-05-10
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Abstract: Abstract A methodological approach is elaborated to study the vascular fluid-tube interaction under pulsatile blood flow within an asymmetrical nonlinear aneurysm and large deformation models. The aneurysm dynamics were modeled using a simplified Lagrangian nonlinear system describing the arterial wall motion with large deformation. The flow is governed by the Navier-Stokes equations in two-dimensional domain. A semi-implicit splitting scheme coupled with the finite difference method is developed to solve the flow equation in an irregular domain using a mesh transformation. On the other hand, the wall equations are solved using the Runge-Kutta method combined with the shooting technique by reducing the resulted boundary value problem to an initial value problem. Rigid and elastic aneurysms are considered and the effect of various geometrical and fluid parameters on the flow are investigated, mainly the Reynolds number, the aneurysm length and height. The study focused on the effect of the asymmetric curvatures of the tube walls and their deformations due to the pulsatile flow. The flow is examined under a steady inlet flow as well as under a pulsatile one for various aneurysm forms. The obtained numerical results validate the fluid and structure solvers and demonstrate significant differences between the rigid and elastic models of the structure as well as the effect of the asymmetric propriety of the arterial aneurysm. PubDate: 2022-05-09
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Abstract: Abstract The aim of this paper is to evaluate the structure of a bi-level system, which consists of multiple leaders at the first level and multiple followers at the second. We integrate the bi-level programming and Data Envelopment Analysis with multiple leaders and followers. The proposed model differs from the existing bi-level Data Envelopment Analysis models in that we use a penalty function for evaluating the cost efficiency instead of the Kuhn–Tucker conditions. So, we first explain the bi-level linear multi-objective programming problem and then utilize an exact penalty method to evaluate the cost efficiencies of decision-making units with multiple leaders and followers. One of the features of our proposed method is that it reduces the number of nonlinear constraints and increases the computational speed compared to existing computational methods. Finally, to demonstrate the efficiency of our method, we provide a numerical example. PubDate: 2022-05-09
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Abstract: Abstract This paper deals with the transmission and spread of the hepatitis A virus in central west Tunisia (the city of Thala). The target of this framework is to determine the global stability of a SEIRD epidemiological model where the infectious compartment is split into symptomatic and asymptomatic compartments. We study the global stability of the equilibrium state using the Lyapunov function which depends on the value of the basic reproduction number \(R_0\) . Therefore, we prove that when \(R_0<1\) , the disease-free equilibrium (DFE) is globally stable, but when \(R_0>1\) , the DFE is unstable, and therefore the the endemic equilibrium is globally stable. PubDate: 2022-05-07
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Abstract: Abstract This manuscript presents the study of local convergence of a seventh order derivative free method in Banach spaces. Earlier study showed the convergence of method using derivatives up to fifth order and only in the n-dimensional Euclidean space. Domain of convergence, computable error bounds and uniqueness of the solution were not studied earlier, thereby limiting the applicability of the method. In present study we focus on these problems and extended the method in more general setting of a Banach space using hypothesis only on the first derivative. Numerical examples are presented to verify the theoretical results. PubDate: 2022-05-05
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Abstract: Abstract Due to the continuous work, degradation in the working capacity of machines and servers is an inevitable phenomenon. To analyze this type of situation in queueing systems, we considered the degradation in the service rate of the server. For the maintenance purpose, vacation is given after completion of a threshold number of services. After maintenance, the server will start working in the fresh mode, that is, with the initial service rate. The impatient behavior of customers and unreliability of the server are also included, which make our model more realistic. We derived the stability condition for this model and found out the steady state probabilities using matrix geometric method. All the system performance measures are calculated. An expected cost function is constructed and is optimized using the particle swarm optimization method. Effects of degrading service rate as well as breakdown rate and vacation rate are studied on the key measures and the expected cost function. PubDate: 2022-05-03
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