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Numerous prior publications on fractional calculus provide fascinating explanations of the theory and applications of fractional calculus operators throughout various mathematical analytic domains. In this paper, we introduce new fractional integral formulas using the Saigo-Maeda fractional integral operators and Appell’s function F3 along with the Srivastava polynomials, the (p,q)-extended Gauss hypergeometric function, and the M-Series. A few fascinating unusual cases of our main conclusions are also considered. This approach can be applied to explore a broad class of previously dispersed discoveries in the literature. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to establish certain generalized Marichev-Saigo-Maeda fractional integral and derivative formulas involving generalized p–extended Hurwitz-Lerch zeta function by using the Hadamard product (or the convolution) of two analytic functions. We then obtain their composition formulas by using fractional integral and derivative formulas and certain Integral transforms associated with Beta, Laplace and Whittaker transforms involving generalized p–extended Hurwitz-Lerch Zeta function. [ABSTRACT FROM AUTHOR]

In this paper, we develop an integer and fractional-order susceptible, infectious, and recovery (SIR) epidemic model based on vital dynamics, i.e., birth, death, immigration, and variable population size, including infection and recovery rates. We investigate the stability analysis for the fractional SIR model on the disease-free and endemic equilibrium points. The existence and uniqueness conditions of solutions for a stable model are also discussed. The residual power series (RPS) approach is used to get the semi-analytical solutions of the proposed model in the form of convergent fractional power series. The convergence analysis of the RPS method is also discussed. Numerical results demonstrate the effect of distinct fractional orders α ∈ (0, 1] on the population density. The obtained results are exciting and may be beneficial for medical experts to control the epidemic disease. [ABSTRACT FROM AUTHOR]

In this paper, mathematical model of heat transfer in a porous fin with internal heat generation, and thermal conductivity is influenced by both spatial factors and temperature are examined. These two concepts are integrated into the model, which highlighting the originality of the current study. The equations and conditions that govern the system are expressed in a dimensionless manner. We examine three scenarios for thermal conductivity: constant, linear, and exponential dependence on temperature. We have utilized three different techniques to solve the problem, including the Legendre Wavelet Collocation, Finite Difference, and Least Square. Due to the nonlinearity of the presented problem, it is not possible to find an exact analytical solution. In this specific scenario, we calculate exact solution, which is then compared to these three methods and found to have a good agreement. The findings and error assessment are displayed in figures and tables. The Legendre wavelet collocation approach yields high accuracy. The novelty of the research is the implantation of space and temperature dependent thermal conductivity and solution of a complex nonlinear problem using a hybrid numerical technique, specifically the collocation method with Legendre Wavelet basis functions. [ABSTRACT FROM AUTHOR]

Hundreds of special functions have been employed in applied mathematics and computing sciences for many centuries due to their outstanding features and wide range of applications. When considering the relevance of these consequences in the evaluation of generalized integrals, applied physics, and many engineering areas, the illustration of image formulas involving one or more variable special functions is significant under various definite integrals. In this paper, it is devoted to study the various integral identities involving incomplete Fox-Wright functions and Srivastava’s polynomials. It is shown that the integrals of the Fox-Wright functions are also the Fox-Wright functions but of greater order. Due to the fact that our results are unified, a substantial number of new results can be constructed as special instances from our leading results. The results obtained in this work are general in nature and very useful in science, engineering and finance. [ABSTRACT FROM AUTHOR]

This study considers in depth the flow of the boundary layer of an incompressible, viscous, and steady Casson fluid through an expanding surface when thermal radiation, heat source, Soret, and Dufour effects are present. Using suitable similarity transformations, the governing non-linear partial differential equations are converted into coupled ordinary differential equations and then estimated using the MATLAB software bvp4c using a shooting process. Variable values of the parameters employed in the current inquiry are offered, together with solutions for the parameters of momentum, temperature, concentration, coefficient of local skin friction, and local Nusselt number. It is observed that the Casson fluid parameter improves fluid velocity and decreases the temperature. Also, it is found that thermal radiation and the presence of a heat source/sink increase the temperature of the fluid. We compared the present investigation with previously published papers and found them harmonious. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to solve Fredholm integral equations (IEs) that involve Sfunction, generalized extended Mittag-Leffler function (GEMLF), and incomplete ℵ-function as the kernel. These types of integral equations appear frequently in applied mathematics, particularly in mathematical physics, engineering, and finance. To solve these integral equations, we employ two powerful mathematical tools, namely fractional calculus (FC) and integral transforms. Specifically, we use the Weyl operator and Mellin transform to solve the integral equation associated with S-functions, GEMLF, and incomplete ℵ-functions. These techniques allow us to express the solution in a closed form, which is essential for practical applications. Moreover, we present several special cases of the solutions obtained, which provide additional insights into the behavior of the solutions. These results are significant for the study of integral equations, as they can be used to derive several known results. Furthermore, the techniques used in this study can be applied to other integral equations that involve different types of functions. [ABSTRACT FROM AUTHOR]

Due to the great success of hypergeometric functions, we provide the analytical solutions of certain definite logarithmic integrals and Nielsen-type integrals in terms of multi-variable Kampé de Fériet functions with suitable convergence conditions and higher harmonic sums by using series rearrangement technique and incomplete Gamma function. Further we also obtain the solution of other related logarithmic integrals in terms of generalized hypergeometric functions and Kummer’s confluent hypergeometric functions by using series rearrangement technique. The results presented in the paper and comparable outcomes are hoped to be supplied by the use of computer-aid programs, for example, Mathematica. [ABSTRACT FROM AUTHOR]

In this paper, the generalization of Simpson’s identity has been derived. This generalized identity has been used to obtain new Hermite-Hadamard inequalities for differentiable convex and quasi-convex functions. Also, the validation of the derived inequalities has been established using suitable examples. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a fully modified (p,q)-poly-Euler polynomials and numbers of the first type. We investigate some properties that is related with (p; q)-Gaussian binomials coefficients. We also construct (p; q)- analogue of the Stirling numbers of the second kind and fully modified (p,q)-poly-Euler polynomials and numbers of the first type with two variables. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of constructing new optimal explicit and implicit Adams-type difference formulas for finding an approximate solution to the Cauchy problem for an ordinary differential equation in a Hilbert space. In this work, I minimize the norm of the error functional of the difference formula with respect to the coefficients, we obtain a system of linear algebraic equations for the coefficients of the difference formulas. This system of equations is reduced to a system of equations in convolution and the system of equations is completely solved using a discrete analog of a differential operator d²/dx² - 1. Here we present an algorithm for constructing optimal explicit and implicit difference formulas in a specific Hilbert space. In addition, comparing the Euler method with optimal explicit and implicit difference formulas, numerical experiments are given. Experiments show that the optimal formulas give a good approximation compared to the Euler method. [ABSTRACT FROM AUTHOR]

In this paper, we construct higher-order q-poly-tangent numbers and polynomials and give several properties, including addition formula and multiplication formula. Finally, we explore the distribution of roots of higher-order q-poly-tangent polynomials. [ABSTRACT FROM AUTHOR]

With this paper, we purpose to introduce and characterized some generalized classes of completely monotone functions on some types of white noise spaces [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study by applying the makgeolli structure to commutative ideal in BCK-algebras. The notion of commutative makgeolli ideal is introduced, and their properties are investigated. The relationship between makgeolli ideal and commutative makgeolli ideal is discussed. Example to show that a makgeolli ideal may not be a commutative makgeolli ideal is provided, and then the conditions under which a makgeolli ideal can be a commutative makgeolli ideal are explored. A new commutative makgeolli ideal is established using the given commutative makgeolli ideal, and characterizations of a commutative makgeolli ideal are displayed. Finally, the extension property for a commutative makgeolli ideal is established. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a general composite iterative algorithm for findinding a common element of the set of solutions of variational inequality problem for a hemicontinuous monotone mapping and the set of fixed points of a hemicontinuous pseudocontractive mapping in a Hilbert space. Under suitable control conditions, we establish strong convergence of the sequence generated by the proposed iterative algorithm to a common element of two sets, which is the unique solution of a certain variational inequality related to a boundedly Lipschitzian and strongly monotone mapping. As a consequence, we obtain the unique minimum-norm common point of two sets. [ABSTRACT FROM AUTHOR]

Fuzzy number (FN) plays a vital role in decision making problems as it is used to represent the uncertain terms. Researchers in the field of decision-making analysis have used triangular and trapezoidal FN to solve the problem in the uncertain environment. FN have also been extended recently such as pentagonal, hexagonal, and heptagonal and so on. This paper aims to generalize the Hexadecagonal fuzzy number (GHFN) which contains set of 16-tuples. Membership functions and alpha cuts of linear and nonlinear GHFN with symmetry and asymmetry have also been derived. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of liner fuzzy real numbers, and show that the set of all positive (or negative) symmetric linear fuzzy real numbers forms a semiring. Moreover, we discuss a complex transform of linear fuzzy real numbers. [ABSTRACT FROM AUTHOR]

In this paper we study linear abstract Cauchy problem in two variables. Theory of two-parameter semigroups of linear operators and tensor product of Banach spaces is needed to study the solution of such equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical result of our algorithm which defined by the hybrid method. [ABSTRACT FROM AUTHOR]

Let H(D) be the set of all analytic functions on the open unit disk D of C, u є H(D) and Φ an entire function on C. In this paper, we characterize the boundedness and compactness of the weighted differentiation superposition operator Dum SΦ from H∞ to the nth weighted-type space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and solve the following additive-additive (s, t)-functional inequality ||g(x+y+z) - g(x) g(y) g(2)|| +||h(x+y+z) + h(x-2y+z) + h(x+y-2z) - 3h(x)||....(0.1) ≤|| s (3g (x+y+z/3)-g(x)-g(y) - g(z)|| + t (3h (x+y+z/3) + h(x-2y+z) + h(x+y-2z) -3h(x)||, wheres and t are fixed nonzero complex numbers with s < 1 and t < 1. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of ternary hom- derivations and ternary homomorphisms in C-ternary algebras, associated to the additive- additive (s, t)-functional inequality (0.1) and the following functional inequality ||g([x, y, z]) [g(x), h(y), h(z)]-[h(x), g(y), h(z)] - [h(x), h(y), g(z)]|| +||h([x, y, z]) - [h(x), h(y), h(z)]|| ≤ φ(x, y, z). [ABSTRACT FROM AUTHOR]

In this paper, we find solutions and investigate the superstability bounded by function for the sine functional equation (S) from the approximate inequality of the Pexider type functional equation: f (x+y/2)²-g(x-y/2)2 = h(x)k(y). Furthermore, the results are extended to Banach algebras. As a consequence, we obtain the superstability for the exponential functional equations, the hyperbolic functional equations, and the jointed Pexider Lobacevski equation. [ABSTRACT FROM AUTHOR]

A Lie point symmetry analysis of a class of higher order difference equations with variable coefficients is considered and new symmetries are found. These symmetries are utilized to investigate the existence of solutions. The results in this paper generalize some results in the literature. [ABSTRACT FROM AUTHOR]

Solitary wave propagation and interaction in plasma using numerical tools like Galerkin Finite Element scheme are discussed in this paper. A one-dimensional nonlinear Schrodinger-Korteweg De-Vries (Sch-KdV) equation is taken as model equation for Non-linear waves propagation in the said media. The derived system, with the help of cubic B-spline source functions are engaged as element and weight functions, after finite element formulation is solved with Runge Kutta Fourth Order method (RK4). Previously the finite element methods with some numerical simulations do not exhibit the complex nature of wave interaction, especially solitary wave interaction. A combination of Galerkin Finite Element scheme with RK4 is a very prominent instrument to study the nature of Non-linear evolution equations in ionic medias, which is the novelty of the paper. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate the stability problems for the following quadratic functional equation f(x+y+z)+f(x+y-z)+f(x-y+z)+f(-x+y+z) = 4f(x)+4f(y)+4f(z) on an unbounded restricted domain. As a consequence, we can apply the obtained results to obtain some asymptotic behaviors of that equation in normed spaces. Moreover, we introduce a new inequality that characterizes the inner product spaces. [ABSTRACT FROM AUTHOR]

The present paper discusses a two-state retrial queueing system with catastrophe. If a customer on arrival finds the server free then it is served immediately. Such customer is known as primary customer. Moreover, if the server is busy then the customer joins virtual queue and retries for service after a random amount of time. This customer is called a secondary customer. Primary and secondary customers both follow Poisson processes. Inter arrival times and service times both follow exponential distribution. Catastrophe occurs on a busy server and its occurrence follows a Poisson process. Catastrophe causes the failure of server and so the server is sent for repair after occurrence of catastrophe. The repair times are also exponentially distributed. Time dependent probabilities for exact number of arrivals in the system and departures from the system when the server is idle or busy are obtained by using recursive approach. The probability of server being under repair is also obtained. Verification of results is done. Numerical results are generated and represented graphically to study the effect of various parameters. [ABSTRACT FROM AUTHOR]

This paper introduces the latest procedure for explaining certain types of fractional wave equations using the variation iteration method (VIM) and Laplace transform. The Laplace variation iteration method is a type of semianalytical technique applied to both linear and non-linear equations without requiring linearization, discretization, or perturbation. It is not a timeconsuming method and converses the solution rapidly with the exact and less error solution. This approach is delineated and then explained through several example cases. The outcomes demonstrate that this alternate strategy yields reliable outcomes and the results are displayed graphically. [ABSTRACT FROM AUTHOR]

The paper presents iterative methods for solving interval linear system of equations. We present a generalization of interval Jacobi method and interval Gauss-Seidel method by generalizing interval diagonal matrices to band interval matrices, and discuss the convergence analysis of the proposed methods. More specifically, we prove that both the proposed methods converge for any initial approximation if the coefficient interval matrix of the system is either an interval strictly diagonally dominant matrix, or interval M-matrix or interval H-matrix. Numerical experiment are carried out to assess the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper we studied Bézier surfaces that are very famous techniques and widely used in Computer Aided Geometric Design. Mainly there are two types of Bézier surfaces which are rectangular and triangular Bézier patches. In this paper we will give a representation for the conversion matrix which converts one type to another. [ABSTRACT FROM AUTHOR]

In this paper, we define fuzzy weak P-property. Then we prove a fuzzy best proximity point theorems for δ-contractions with condition fuzzy weak P-property. Later, we give definition of fuzzy isometric distance between two functions in non-Archimedean fuzzy metric spaces. Also, we introduce δ-proximal contraction type-1 and type-2 contraction respectively via functions preserving fuzzy isometric distance and providing fuzzy isometry. Then, we obtain some fuzzy best proximity results for -proximal contractions types in non-Archimedean fuzzy metric spaces. Finally, we present some examples to illustrate the validity of the definitions and results obtained in the paper. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find exact solutions for the conformable fractional Harry Dym Equation. In this work we deal with three different forms of conformable fractional Harry Dym Equation and for each form a suitable wave variable substitution is found. Each substitution transform its corresponding problem to an ordinary differential equation, What is more, the resulted ordinary differential equations in the three cases are the same. General solutions are obtained by applying the direct integration method on the resulted ordinary differential equation. These obtained solutions are found for some particular choices for the constants values. The behavior of every solution is discussed and illustrated in graphs. The tedious integrals and difficult computations associated with calculations in this paper are performed and simplified by using Mathematica 9.0. [ABSTRACT FROM AUTHOR]

Co-ordinated convex function of two variables and corresponding inequalities have been studied before by many researchers. This paper deals with Co-ordinated convex function of three variables. In the present paper the idea of co-ordinated convex function of two variables in a rectangle from the plane R² is extended to that of three variables in a rectangle from space R³. Moreover corresponding extended right handed Hermite-Hadamard type inequalities are also incorporated. At the end some applications of resulting inequalities to special means are also given. [ABSTRACT FROM AUTHOR]

This paper discusses the principle, design and theoretical dynamical modelling of MEMS capacitive pressure sensors with different material properties results that have been simulated as well as compared. The properties of the material ensure that sensor performance analysis for operating pressure range 0-25kPa. This work discusses Timoshenkos plate deflection theory and follows the pull-in phenomenon. One important factor that could influence the performance of a MEMS capacitive pressure sensor is the structure of the diaphragm. The active area of this sensor is made up of 0.5 mm0.5 mm and the cavity size are 2m. According to the simulations, the optimized parameters have higher linearity and greater sensitivity than the initial parameters. The comparison of results shows that Aluminium material gives the highest deflection and better capacitance sensitivities which is about 88 pF/pa and is more linear with the applied pressure than other materials. The behaviour of the touch mode capacitive pressure sensor in terms of the temperature dependence of capacitance is analysed and repeatability error has been reduced. This configuration of touch mode pressure sensor is promising for the use in health monitoring devices like patient blood pressure due to small pressure fluctuation. [ABSTRACT FROM AUTHOR]

This paper presents the tripled system of differential equations of fractional type with fractional integral boundary conditions as well as integer and fractional derivative. Here the Banach fixed points theorem and Scheafer's fixed points theorem are used as a main tool. To justify the results we illustrate some examples. [ABSTRACT FROM AUTHOR]

For solving non-linear equations, iterative root-finding methods are important because of the broad range of applications in science and engineering. We have constructed an iterative method based on multiplicative calculus in this paper. Some numerical results are performed to exposed the efficiency of proposed and earlier method. [ABSTRACT FROM AUTHOR]

In this paper, we present a explicit viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorem of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

This paper introduces the latest procedure for explaining certain types of fractional wave equations using the variation iteration method (VIM) and Laplace transform. The Laplace variation iteration method is a type of semi-analytical technique applied to both linear and non-linear equations without requiring linearization, discretization, or perturbation. It is not a time-consuming method and converses the solution rapidly with the exact and less error solution. This approach is delineated and then explained through several example cases. The outcomes demonstrate that this alternate strategy yields reliable outcomes and the results are displayed graphically. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate the stability problems for the following quadratic functional equation f(x+y+z)+f(x+y-z)+f(x-y+z)+f(-x+y+z) = 4f(x)+4f(y)+4f(z) on an unbounded restricted domain. As a consequence, we can apply the obtained results to obtain some asymptotic behaviors of that equation in normed spaces. Moreover, we introduce a new inequality that characterizes the inner product spaces. [ABSTRACT FROM AUTHOR]

The present paper discusses a two-state retrial queueing system with catastrophe. If a customer on arrival finds the server free then it is served immediately. Such customer is known as primary customer. Moreover, if the server is busy then the customer joins virtual queue and retries for service after a random amount of time. This customer is called a secondary customer. Primary and secondary customers both follow Poisson processes. Inter arrival times and service times both follow exponential distribution. Catastrophe occurs on a busy server and its occurrence follows a Poisson process. Catastrophe causes the failure of server and so the server is sent for repair after occurrence of catastrophe. The repair times are also exponentially distributed. Time dependent probabilities for exact number of arrivals in the system and departures from the system when the server is idle or busy are obtained by using recursive approach. The probability of server being under repair is also obtained. Verification of results is done. Numerical results are generated and represented graphically to study the effect of various parameters. [ABSTRACT FROM AUTHOR]

The paper presents iterative methods for solving interval linear system of equations. We present a generalization of interval Jacobi method and interval Gauss-Seidel method by generalizing interval diagonal matrices to band interval matrices, and discuss the convergence analysis of the proposed methods. More specifically, we prove that both the proposed methods converge for any initial approximation if the coefficient interval matrix of the system is either an interval strictly diagonally dominant matrix, or interval M-matrix or interval H-matrix. Numerical experiment are carried out to assess the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper discusses the principle, design and theoretical dynamical modelling of MEMS capacitive pressure sensors with different material properties results that have been simulated as well as compared. The properties of the material ensure that sensor performance analysis for operating pressure range 0-25kPa. This work discusses Timoshenkos plate deflection theory and follows the pull-in phenomenon. One important factor that could influence the performance of a MEMS capacitive pressure sensor is the structure of the diaphragm. The active area of this sensor is made up of 0.5 mm 0.5 mm and the cavity size are 2m. According to the simulations, the optimized parameters have higher linearity and greater sensitivity than the initial parameters. The comparison of results shows that Aluminium material gives the highest deflection and better capacitance sensitivities which is about 88 pF/pa and is more linear with the applied pressure than other materials. The behaviour of the touch mode capacitive pressure sensor in terms of the temperature dependence of capacitance is analysed and repeatability error has been reduced. This configuration of touch mode pressure sensor is promising for the use in health monitoring devices like patient blood pressure due to small pressure fluctuation. [ABSTRACT FROM AUTHOR]

In this paper, Mexican hat wavelet transformation is defined on the space of tempered generalized quotients by employing the structure of exchange property. We study the exchange property for the Mexican hat wavelet transform by applying the theory of the Mexican hat wavelet transform of distributions. Further, different properties of Mexican hat wavelet transform are investigated on the space of tempered generalized quotients. [ABSTRACT FROM AUTHOR]

This paper presents the tripled system of differential equations of fractional type with fractional integral boundary conditions as well as integer and fractional derivative. Here the Banach fixed points theorem and Scheafer's fixed points theorem are used as a main tool. To justify the results we illustrate some examples. [ABSTRACT FROM AUTHOR]

For solving non-linear equations, iterative root-finding methods are important because of the broad range of applications in science and engineering. We have constructed an iterative method based on multiplicative calculus in this paper. Some numerical results are performed to exposed the efficiency of proposed and earlier method. [ABSTRACT FROM AUTHOR]

In this paper, we have projected the theoretical and numerical investigation of the mathematical model representing the yellow fever virus transmission from infected mosquitoes to humans or vise-versa through mosquito bites in the framework of the Caputo derivative. Theoretical aspects of the dynamics of susceptible individuals, exposed individuals, infected individuals, toxic infected individuals, recovered and immune individuals, and susceptible mosquitoes and infected mosquitoes have been analyzed by using the theory of fractional calculus such as boundedness, uniqueness and existence of the solutions. Sufficient conditions for the global stability of the virus-free point of equilibrium are inspected. T validate the theoretical results numerical analysis is performed using the generalized Adams-Bashforth-Moultan method. [ABSTRACT FROM AUTHOR]

In multi-objective transportation, due to the conflicting nature of objectives, no method is available to find the best compromise optimal solution. In this paper, we present a method to obtain a compromised solution for multi-objective transportation problems under a weighted environment. In which, a modified weighted model is presented that provides us with an efficient solution according to the priorities of the decision maker. To measure the efficiency of the method, a numerical example is included and the results are compared with previously reported work for the same numerical problems to illustrate the feasibility and the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we construct some new image formulas for the incomplete H-and ...-functions under the Akel's M-transform. We also provide image formulas for the incomplete Meijer's G-functions, incomplete Fox-Wright functions and Fox's H-function, as special cases of our main findings in corollaries. [ABSTRACT FROM AUTHOR]

The onset of Maxwell-Cattaneo DDC in a viscoelastic fluid layer is studied using linear stability analysis with the help of normal mode technique. The parabolic advection diffusion equation, which presupposes classical fickian diffusion for both heat and salt, controls the evaluation of temperature and salinity. Analytically, the onset criteria for stationary and oscillatory convection is derived. Since the onset of stationary (steady case) convection is unaffected by Maxwell-Cattaneo effects as well as visco-elastic parameters, oscillatory convection rather than stationary convection is the key to visualize the effects of different parameters in this paper. Two different scenarios for oscillatory convection have been discussed (i) when Maxwell-Cattaneo coefficient for salinity CS = 0 and (ii) when Maxwell-Cattaneo coefficient for temperature CT = 0. Also a comparative study for these two cases i.e. CS = 0 and CT = 0 is performed for different controlling parameters like relaxation parameter (λ1), retardation parameter (λ2), diffusion ratio (τ), solutal Rayleigh number (RaS) and Prandtl number (Pr) with the help of graphs. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solution of space fractional Burger's equation using the implicit finite difference scheme and Lax-Friedrichs- implicit finite difference scheme respectively. The Riemann-Liouville based fractional derivative (non-integer order) is fitted for the diffusion term of fractional order 1:0 < α ≤ 2:0. The Mathematical induction is used to es- timate a stability of both the implicit and Lax-Friedrichs-implicit schemes. The study shows that the implicit based scheme is stable and the results are good in agreement with the exact solution. Finally, the significance of space fractional order with respect to the solution is discussed. It is noted that the solution of space fractional Burger's equation get affected by changing the space fractional order. [ABSTRACT FROM AUTHOR]