Browsing by Author "Siddique, Imran"

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A Drone-Based Blood Donation Approach Using an Ant Colony Optimization Algorithm
(2023) Jarad, Fahd; Ashraf, Faraha; Jarad, Fahd; Sardar, Muhammad Shoaib; Siddique, Imran; 234808
This article presents an optimized approach of mathematical techniques in the medical domain by manoeuvring the phenomenon of ant colony optimization algorithm (also known as ACO). A complete graph of blood banks and a path that covers all the blood banks without repeating any link is required by applying the Travelling Salesman Problem (often TSP). The wide use promises to accelerate and offers the opportunity to cultivate health care, particularly in remote or unmerited environments by shrinking lab testing reversal times, empowering just-in-time lifesaving medical supply.
A Novel Multicriteria Decision-Making Approach for Einstein Weighted Average Operator under Pythagorean Fuzzy Hypersoft Environment
(2022) Jarad, Fahd; Jarad, Fahd; Majdoubi, Jihen; Zulqarnain, Rana Muhammad; Iampan, Aiyared; Siddique, Imran; 234808
The experts used the Pythagorean fuzzy hypersoft set (PFHSS) in their research to discourse ambiguous and vague information in decision-making processes. The aggregation operator (AO) plays a prominent part in the sensitivity of the two forefront loops and eliminates anxiety from that perception. The PFHSS is the most influential and operative extension of the Pythagorean fuzzy soft set (PFSS), which handles the subparameterized values of alternatives. It is also a generalized form of Intuitionistic fuzzy hypersoft set (IFHSS) that provides better and more accurate assessments in the decision-making (DM) process. In this work, we present some operational laws for Pythagorean fuzzy hypersoft numbers (PFHSNs) and then formulate Pythagorean fuzzy hypersoft Einstein weighted average (PFHSEWA) operator based on developed operational laws. We discuss essential features such as idempotency, boundedness, and homogeneity for the proposed PFHSEWA operator. Furthermore, a DM approach has been developed based on the built-in operator to address multicriteria decision-making (MCDM) issues. A numerical case study of decision-making problems in real-life agricultural farming is considered to validate the settled technique's dominance and applicability. The consequences display that the planned model is more operative and consistent to handle inexact data based on PFHSS.
A Survey on Generalized Topological Indices for Silicon Carbide Structure
(2022) Jarad, Fahd; Altunok, Taner; Mahboob, Abid; Siddique, Imran; Altunok, Taner; 234808
The application of graphs in chemical and molecular structures has exponentially increased during the last few years. Topological indices facilitate the collection of beneficial information and provide an approach to understanding the properties of chemical structure by providing information about algebraic graphs. Let G be a graph with u-vertices and Ωu be the degree of uth vertex. In this manuscript, we compute Zagreb index (ZI), first, and second, Hyper F-indices and sum and product connectivity of F-index of silicon carbides, namely, SiC4 - I[r, s] and SiC4 - II[r, s].
AggregationOperators for Interval-Valued Pythagorean FuzzyHypersoft Set with Their Application to SolveMCDMProblem
(2023) Jarad, Fahd; Siddique, Imran; Ali, Rifaqat; Jarad, Fahd; Iampan, Aiyared; 234808
Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of intervalvalued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDMtechnique is deliberate formaterial selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projectedMCGDMmethod for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.
An Approach of Decision-Making under the Framework of Fermatean Fuzzy Sets
(2022) Jarad, Fahd; Altunok, Taner; Ahsan, Muhammad; Jarad, Fahd; Altunok, Taner; 234808
Because of its influence on various elements of human life experiences and conditions, the building industry is a significant business. In the recent past, environmental considerations have been incorporated in the design and planning stages of building supply chains. The process of evaluating and selecting suppliers is one of the most important issues in supply chain management. A multicriteria decision-making (MCDM) problem can be utilized to handle such issues. The goal of this research is to present a new and efficient technique for selecting suppliers with ambiguous data. The suggested methodology's structure is based on technology for order of preference by similarity to ideal solution (TOPSIS), with Fermatean fuzzy sets (Fr FSs) employed to cope with information uncertainty. In this article, authors modified the distance between Fr FSs to propose the similarity measure and implemented it to form the MCDM model to resolve the vague and uncertain data. Moreover, we used this similarity measure to choose the optimal alternative. A practical example for alternative selection is provided, along with a comparison of the acquired findings to existing approach. Finally, to strengthen the outcome obtained through the proposed model, sensitivity analysis and time complexity analysis are performed.
Analysis of Natural Convection in Nanofluid Flow through a Channel with Source/Sink Effect
(2022) Jarad, Fahd; Sadiq, Kashif; Jarad, Fahd; Al Mesfer, Mohammed K.; Danish, Mohd; Yaqoob, Sonia; 234808
In this study, the natural convection nanofluids flow through a channel formed by two vertical parallel plates having distance d between them has been examined under the influence of the ramped velocity. Sodium alginate is considered as base fluid, and nanoparticles of titania (TiO2) and alumina (Al2O3) are added to it. Analytical and semianalytical results for temperature and velocity profiles are obtained with Laplace transform and inverse Laplace algorithms (Tzou, Stehfest, Talbot, Honig and Hirdes, and Fourier series), respectively. Furthermore, the impacts of nanoparticles, Prendtl number, heat absorption, and time on velocity and temperature are drawn graphically and discussed. The outcomes show that the high thermal conductivity of particles increases the temperatures, and the high density of particles decreases the velocities of the nanofluids. The current findings are compared to previous findings in the literature. In the tables, the effect of volume fraction on Nusselt numbers and skin frictions is explored.
Bioconvection attribution for effective thermal transportation of upper convicted Maxwell nanofluid flow due to an extending cylindrical surface
(2022) Jarad, Fahd; Siddique, Imran; Abdal, Sohaib; Jarad, Fahd; Ali, Rifaqat; Salamat, Nadeem; Hussain, Sajjad; 234808
The growth of compact density heat gadgets demands effective thermal transportation. The option of nanofluid plays a dynamic role in this requirement. This research shows the impact of gyrotactic microorganisms on non-Newtonian fluid (Maxwell fluid) passing on the expanding cylindrical surface. The main objective of the present observation is to determine the heat and mass transportation of Maxwell nanofluid. The convective boundary condition and zero mass flux conditions are incorporated. In mathematical derivation, the approximation of the boundary layer is applied. The primal motivation pertains to exaggerating the thermal transport of heat exchangers in industrial processes. To attain the effects of Brownian motion as well as thermophoresis the Buongiorno nanofluid is utilized. By assimilating suitable transformation, the concluding simultaneous for a non-linear set of equations is tackled numerically by hiring Runge-Kutta procedure. The coding is developed and run in the Matlab environment. The leading partial differential system is converted into an ordinary differential system. The role of emerging parameters is elaborated. Also tangible quantities i.e. Skin friction factor, Nusselt number, Sherwood number, and motile density coefficient are enumerated. An accession in the magnetic field causes depreciation in the velocity profile. Where increment in Schmidt number Sc causes a decrement in Sherwood number. The suitable ranges of parameters where increasing or decreasing behavior becomes smooth are taken as 0.0 ≤ M ≤ 6.0, 0.0 ≤ γ≤ 0.8, 0.7 ≤ Pr ≤ 1.0, 0.1 ≤ Nt ≤ 0.7, 0.01 ≤ Nb ≤ 0.1, 3.0 ≤ Sc ≤ 6.0, 2.0 ≤ Lb ≤ 7.0, 0.1 ≤ Pe ≤ 0.7 and 1.0 ≤ δ≤ 7.0. The applications of the current study can be seen in chemical and metallurgical industries, the process of thermo-fluid, power generation, executed via condensers, cooling, and heating in large buildings, transportation, etc.
Bioconvection of MHD Second-Grade Fluid Conveying Nanoparticles over an Exponentially Stretching Sheet: A Biofuel Applications
(2023) Jarad, Fahd; Nadeem, Muhammad; Ali, Rifaqat; Jarad, Fahd; 234808
The current research examines the role of chemical reaction, nonlinear thermal radiation and slippage impact on magnetic second-grade fluid flow with diluted dispersion of nanoparticles using a theoretical bioconvection model over an exponentially stretched sheet. There are also new characteristics such as Brownian motion and thermophoresis. In the problem formulation, the boundary layer approximation is used. Using the suitable transformations, the energy, momentum, micro-organisms and concentration equations are generated into nonlinear ordinary differential equations (ODEs). The solution to the resultant problems was calculated via the Homotopy analysis method (HAM). Environmental parameters' effects on velocity, temperature, microbes and concentration profiles are graphically displayed. When comparing the current results to the previous literature, there was also a satisfactory level of agreement. In comparison with a flow based on constant characteristics, the flow with variable thermal conductivity is shown to be significantly different and realistic. The temperature and motile density of the fluid grew in direct proportion to the thermophoresis motion, buoyancy ratio and Brownian motion parameters. Also, the motile density profile decreases down for Pe and Lb while increasing when bioconvection Rayleigh number and buoyancy ratio. This work is significant to bioinspired nanofluid enhanced fuel cells and nanomaterials production techniques, according to these research studies.
Boger nanofluid: significance of Coriolis and Lorentz forces on dynamics of rotating fluid subject to suction/injection via finite element simulation
(2022) Baleanu, Dumitru; Siddique, Imran; Hussain, Sajjad; Ali, Liaqat; Baleanu, Dumitru; 56389
This study briefings the roles of Coriolis, and Lorentz forces on the dynamics of rotating nanofluids flow toward a continuously stretching sheet. The nanoparticles are incorporated because of their unusual qualities like upgrade the thermal transportation, which are very important in heat exchangers, modern nanotechnology, electronics, and material sciences. The primary goal of this study is to improve heat transportation. Appropriate similarity transformations are applied for the principal PDEs to transform into nonlinear dimensionless PDEs. A widely recognized Numerical scheme known as the Finite Element Method is employed to solve the resultant convective boundary layer balances. Higher input in the solvent fraction parameter has a rising effect on the primary velocity and secondary velocity magnitude, and decreasing impact on the distributions of temperature. It is seen that growing contributions of the Coriolis, and Lorentz forces cause to moderate the primary and secondary velocities, but the temperature and concentration functions show opposite trend. The concentration, temperature, and velocities distributions for suction case is prominently than that of injection case, but inverse trend is observed for local Nusselt and Sherwood numbers. These examinations are relevant to the field of plastic films, crystal growing, paper production, heat exchanger, and bio-medicine.
Case Studies in Thermal Engineering
(2022) Jarad, Fahd; Siddique, Imran; Ali, Rifaqat; Jarad, Fahd; Abdal, Sohaib; Hussain, Sajjad; 234808
We scrutinized the influence of nonlinear heat radiation on heat transmission evaluation of Carreau nanofluid and tangent hyperbolic nanofluid streams across a wedge with gyrotactic microorganisms by taking slip situations into consideration in this research article. The necessary nonlinear partial differential formulation is transmuted into non-linear ordinary differential equations by employing appropriate similarity variables, and these equations, including the boundary constraints are resolved in Matlab software utilizing Runge-Kutta fourth order via shooting tactic. A definite description of the framework is achieved by fluctuating the inputs of influential variables of the dependent functions and exhibited via graphs. The inhibiting flow velocity is portrayed by the intensifying inputs of buoyancy ratio, magnetic force, Rayleigh number, and eigenvalue. As a consequence of thermophoresis and Brownian motion of nano-particles, the temperature of the liquids initiates to ascend instantly. Because of differentiated viscous effects, the flow velocity for Carreau nanofluid is slower than that of tangent hyperbolic fluid and the temperature behavior is reversed. Further, the magnitude of skin friction factor for tangent hyperbolic nanofluid is almost half ofs that of Carreau nanofluid.
Computation of Vertex-Based Topological Indices of Middle Graph of Alkane CtH2t+2
(2022) Jarad, Fahd; Türkan, Erkan Murat; Jarad, Fahd; Ali, Muhammad Asad; Türkan, Erkan Murat; Danish, Muhammad; 234808
Alkanes are the primary constituents of methane or natural gas that can also be found in volcanic crust. As a result of methane as a heat source, humans may cook without using any fuel in a volcanic environment. Propane which is an alkane derivative is safer alternative to methane and is commonly present in gas cooking fuel, as well as a tiny amount of gasoline and matches. The primary ingredient in automobile especially gasoline is also alkane in the form of octane. Topological indices are largely applied in chemistry to improve the quantitative structure relationship in which the properties of the molecules can be linked with their chemical structures. In this research work, we will calculate the certain well-known topological indices of the middle graph of alkane based on vertex degree and also present a numerical and graphical comparison of computed topological indices.
Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics
(2022) Jarad, Fahd; Mirza, Arshad M.; Shahzadi, Kausar; Akbar, M. Ali; Jarad, Fahd; 234808
In this paper, we obtain the novel exact traveling wave solutions in the form of trigonometric, hyperbolic and exponential functions for the nonlinear time fractional generalized reaction Duffing model and density dependent fractional diffusion-reaction equation in the sense of beta-derivative by using three fertile methods, namely, Generalized tanh (GT) method, Generalized Bernoulli (GB) sub-ODE method, and Riccati-Bernoulli (RB) sub-ODE method. The derived solutions to the aforementioned equations are validated through symbolic soft computations. To promote the vital propagated features; some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the specific values to the parameters under the confine conditions. The accomplished solutions show that the presented methods are not only powerful mathematical tools for generating more solutions of nonlinear time fractional partial differential equations but also can be applied to nonlinear space-time fractional partial differential equations.
Dufour Effect on Transient MHD Double Convection Flow of Fractionalized Second-Grade Fluid with Caputo-Fabrizio Derivative
(2021) Jarad, Fahd; Ayaz, Sehrish; Jarad, Fahd; 234808
This article presents the problem, in which we study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid flow in the presence of heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. The constitutive equations for the mass flux and thermal flux are modeled for noninteger-order derivative Caputo-Fabrizio (CF) with nonsingular kernel, respectively. The Laplace transform and Laplace inversion numerical algorithms are used to derive the analytical and semianalytical solutions for the dimensionless concentration, temperature, and velocity fields. Expressions for the skin friction and rates of heat and mass transfer from the plate to fluid with noninteger and integer orders, respectively, are also determined. Furthermore, the influence of flow parameters and fractional parameters alpha and beta on the concentration, temperature, and velocity fields are tabularly and graphically underlined and discussed. Furthermore, a comparison between second-grade and viscous fluids for noninteger and integer is also depicted. It is observed that integer-order fluids have greater velocities than noninteger-order fluids. This shows how the fractional parameters affect the fluid flow.
Einstein Aggregation Operators for Pythagorean Fuzzy Soft Sets with Their Application in Multiattribute Group Decision-Making
(2022) Jarad, Fahd; Siddique, Imran; Jarad, Fahd; Hamed, Y.S.; Abualnaja, Khadijah M.; Iampan, Aiyared; 234808
The Pythagorean fuzzy soft set (PFSS) is the most proficient and manipulative leeway of the Pythagorean fuzzy set (PFS), which contracts with parameterized values of the alternatives. It is a generalized form of the intuitionistic fuzzy soft set (IFSS), which provides healthier and more accurate evaluations through decision-making (DM). The main determination of this research is to prolong the idea of Einstein's aggregation operators for PFSS. We introduce the Einstein operational laws for Pythagorean fuzzy soft numbers (PFSNs). Based on Einstein operational laws, we construct two novel aggregation operators (AOs) such as Pythagorean fuzzy soft Einstein-weighted averaging (PFSEWA) and Pythagorean fuzzy soft Einstein-weighted geometric (PFSEWG) operators. In addition, important possessions of proposed operators, such as idempotency, boundedness, and homogeneity, are discussed. Furthermore, to validate the practicability of the anticipated operators, a multiple attribute group decision-making (MAGDM) method is developed. We intend innovative AOs considering the Einstein norms for PFSS to elect the most subtle business. Pythagorean fuzzy soft numbers (PFSNs) support us to signify unclear data in real-world perception. Furthermore, a numerical description is planned to certify the efficacy and usability of the projected method in the DM practice. The recent approach's pragmatism, usefulness, and tractability are validated through comparative exploration with the support of some prevalent studies.
Einstein Weighted Geometric Operator for Pythagorean Fuzzy Hypersoft with Its Application in Material Selection
(2023) Jarad, Fahd; Siddique, Imran; Ali, Rifaqat; Jarad, Fahd; Iampan, Aiyared
Hypersoft set theory is a most advanced form of soft set theory and an innovative mathematical tool for dealing with unclear complications. Pythagorean fuzzy hypersoft set (PFHSS) is the most influential and capable leeway of the hypersoft set (HSS) and Pythagorean fuzzy soft set (PFSS). It is also a general form of the intuitionistic fuzzy hypersoft set (IFHSS), which provides a better and more perfect assessment of the decision-making (DM) process. The fundamental objective of this work is to enrich the precision of decision-making. A novel mixed aggregation operator called Pythagorean fuzzy hypersoft Einstein weighted geometric (PFHSEWG) based on Einstein's operational laws has been developed. Some necessary properties, such as idempotency, boundedness, and homogeneity, have been presented for the anticipated PFHSEWG operator. Multi-criteria decision-making (MCDM) plays an active role in dealing with the complications of manufacturing design for material selection. However, conventional methods ofMCDMusually produce inconsistent results. Based on the proposed PFHSEWG operator, a robust MCDM procedure for material selection in manufacturing design is planned to address these inconveniences. The expected MCDM method for material selection (MS) of cryogenic storing vessels has been established in the real world. Significantly, the planned model for handling inaccurate data based on PFHSS is more operative and consistent.
Engine oil based MoS2Casson nanofluid flow with ramped boundary conditions and thermal radiation through a channel
(2022) Jarad, Fahd; Sadiq, Kashif; Jaradat, Mohammed M.M.; Ali, Rifaqat; Jarad, Fahd; 234808
The modern era is a time to have cost-effective and energy-efficient technology. This demand has made nanotechnology the most effective field. The focus of this article is to increase the efficiency of engine oil (EO). The flow of EO-based Casson nanofluid containing Molybdenum disulfide (MoS2) nanoparticles is investigated with ramped wall conditions and thermal radiation. Analytical results are calculated via the Laplace transform. The impact of physical parameters on isothermal and ramped conditions is illustrated graphically and discussed in detail. The researchers found that flow, mass, and energy can be controlled by using ramped conditions. The variation in concentration, temperature, and velocity is exponential for isothermal conditions and steady for ramped wall conditions. Finally, the results of Nusselt numbers, skin frictions, and Sherwood numbers on both walls of the channel for both isothermal and ramped conditions are graphically depicted and discussed. For higher values of time the results of ramped and isothermal wall conditions are identical. It is found that the nanoparticles of MoS2 enhance the lubrication and heat transport rates of EO.
Extension of aggregation operators to site selection for solid waste management under neutrosophic hypersoft set
(2023) Jarad, Fahd; Ma, Wen Xiu; Siddique, Imran; Gurmani, Shahid Hussain; Jarad, Fahd; Ahamad, Muhammad Irfan; 234808
With the fast growth of the economy and rapid urbanization, the waste produced by the urban population also rises as the population increases. Due to communal, ecological, and financial constrictions, indicating a landfill site has become perplexing. Also, the choice of the landfill site is oppressed with vagueness and complexity due to the deficiency of information from experts and the existence of indeterminate data in the decision-making (DM) process. The neutrosophic hypersoft set (NHSS) is the most generalized form of the neutrosophic soft set, which deals with the multi-sub-attributes of the alternatives. The NHSS accurately judges the insufficiencies, concerns, and hesitation in the DM process compared to IFHSS and PFHSS, considering the truthiness, falsity, and indeterminacy of each sub-attribute of given parameters. This research extant the operational laws for neutrosophic hypersoft numbers (NHSNs). Furthermore, we introduce the aggregation operators (AOs) for NHSS, such as neutrosophic hypersoft weighted average (NHSWA) and neutrosophic hypersoft weighted geometric (NHSWG) operators, with their necessary properties. Also, a novel multi-criteria decision-making (MCDM) approach has been developed for site selection of solid waste management (SWM). Moreover, a numerical description is presented to confirm the reliability and usability of the proposed technique. The output of the advocated algorithm is compared with the related models already established to regulate the favorable features of the planned study.
Extension of Einstein Average Aggregation Operators to Medical Diagnostic Approach Under q-Rung Orthopair Fuzzy Soft Se
(2022) Jarad, Fahd; Rehman, Hafiz Khalil Ur; Awrejcewicz, Jan; Ali, Rifaqat; Siddique, Imran; Jarad, Fahd; Iampan, Aiyared; 234808
The paradigm of the soft set (SS) was pioneered by Moldotsov in 1999 by prefixing the parametrization tool in accustomed sets, which yields general anatomy in decision-making (DM) problems. The q-rung orthopair fuzzy soft set (q-ROFSS) is an induced form of the intuitionistic fuzzy soft set (IFSS) and Pythagorean fuzzy soft set (PFSS). It is also a more significant structure to tackle complex and vague information in DM problems than IFSS and PFSS. This manuscript explores new notions based on Einstein's operational laws for q-rung orthopair fuzzy soft numbers (q-ROFSNs). Our main contribution is to investigate some average aggregation operators (AOs), such as q-rung orthopair fuzzy soft Einstein weighted average (q-ROFSEWA) and q-rung orthopair fuzzy soft Einstein ordered weighted average (q-ROFSEOWA) operators. Besides, the fundamental axioms of proposed operators are discussed. Multi-criteria group decision-making (MCGDM) is vigorous in dealing with the compactness of real-world obstacles, and still, the prevailing MCGDM methods constantly convey conflicting consequences. Based on offered AOs, a robust MCGDM approach is deliberated to accommodate the defects of the prevalent MCGDM methodologies under the q-ROFSS setting. Based on the planned MCGDM method, a medical diagnostic procedure is implemented to recognize the nature of certain infections in different patients. The protracted model estimates illustrious score values to determine patients' health compared to prevailing models, which is more helpful for healthcare experts in identifying the severity of diseases in patients. Furthermore, an inclusive comparative analysis is accomplished to ratify the pragmatism and effectiveness of the proposed technique with some formerly standing methods. The consequences gained over comparative studies display that our established method is more proficient than predominant methodologies.
Impact of Ramped Concentration and Temperature on MHD Casson Nanofluid Flow through a Vertical Channel
(2021) Jarad, Fahd; Siddique, Imran; Ali, Rifaqat; Jarad, Fahd; 234808
The mass and heat transport of Casson nanofluid flow in a channel under the influence of the magnetic field, heat generation, chemical reaction, ramped concentration, and ramped temperature is studied. Nanoparticles of copper (Cu) are inserted in sodium alginate (SA) to make nanofluid. The definition of time-fractional Caputo derivative is applied to have the fractional model. The analytical results of concentration, temperature, velocity, skin friction, Sherwood numbers, and Nusselt numbers for ramped and isothermal boundary conditions are obtained in the form of summation after applying the Laplace inverse transform. The effects of the fractional parameter (ξ) and physical parameters are depicted graphically. For higher values of ξ the velocity, concentration and temperature reduce. The fractional model is a better choice to control velocity, concentration, and temperature profiles. The energy enhances by increasing volume fraction (φ), whereas mass and flow of nanofluid reduce. The Sherwood and Nusselt numbers for both isothermal and ramped conditions increase by increasing φ. Ramped conditions can control the flow, mass, and heat of the nanofluid. © 2021 Kashif Sadiq et al.
Meshfree numerical integration for some challenging multi-term fractional order PDEs
(2022) Jarad, Fahd; Siddique, Imran; Jarad, Fahd; 234808
Fractional partial differential equations (PDEs) have key role in many physical, chemical, biological and economic problems. Different numerical techniques have been adopted to deal the multi-term FPDEs. In this article, the meshfree numerical scheme, Radial basis function (RBF) is discussed for some time-space fractional PDEs. The meshfree RBF method base on the Gaussian function and is used to test the numerical results of the time-space fractional PDE problems. Riesz fractional derivative and Grünwald-Letnikov fractional derivative techniques are used to deal the space fractional derivative terms while the time-fractional derivatives are iterated by Caputo derivative method. The accuracy of the suggested scheme is analyzed by using L∞-norm. Stability and convergence analysis are also discussed.