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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]

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 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 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]

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 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]

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]

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]

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]

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]

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 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]

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]

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 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]

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]

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 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]

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 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]

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]

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]

The Covid-19 outbreak hit us as a serious health crisis with vaccination to be seen as the only way out of it. And media can play the role of an advocate to fight against this epidemic by spreading important awareness regarding various protocols and vaccination strategies. Since breakthrough infections are becoming highly common, a two dose vaccine regime may be the need of the hour even for individuals with a pre-existing illness to build better immunity. Thus in this paper, our aim is to analyse a mathematical model with two dose vaccination strategy in the presence of media and breakthrough infections. An SIV1V2R model is formulated and the dynamical analysis is done. The basic reproduction number is obtained and the local stability analysis of both the disease-free and endemic equilibrium point is discussed based on reproduction number. The global stability of the endemic equilibrium point is done by graph theoretic approach. Finally, the numerical validation of the analytic solution is done using MATLAB using the real data of India for some important parameters to address a few vital questions which involves the role of media on the vaccination strategy. And sensitive model parameters effecting the basic reproduction number and endemic equilibrium points are identified using sensitivity analysis techniques like PRCC(partial rank correlation coefficient). Thus, the outcomes demonstrated the trend a two-dose vaccine model can follow and how the effect of media can help bring down the infections. This model provides support that two dose vaccination against COVID-19 with media presence for awareness is highly effective in controlling this epidemic. [ABSTRACT FROM AUTHOR]

Recently, the idea of φ-fixed point and the elementary results on φ-fixed points were first investigated by Jleli et al. [Jleli M, Samet B, Vetro C (2014) Fixed point theory in partial metric spaces via φ-fixed point's con- cept in metric spaces. Journal of Inequalities and Applications, 2014(1):1- 9.]. Based on this work, Karapinar et al. [Karapinar E, O'Regan D, Samet B (2015) On the existence of fixed points that belong to the zero set of a certain function. Fixed Point Theory and Applications, 2015(1):1-14.] established the new φ-fixed point results, which can be reduced to the famous fixed point result of Boyd and Wong in 1969. However, the main result of Karapinar et al. does not cover the φ-fixed point results of Jleli et al. This paper aims to fulfill this gap by proving φ-fixed point results covering several φ-fixed point results and fixed point results [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]

In this paper, two-parameter singularly perturbed parabolic equations are examined by two level method using non-polynomial spline. We have used non-polynomial quadratic spline in space and finite difference discretization in time. Stability analysis is carried out. The approximate solution is shown to converge point-wise to the true solution. Numerical solution of singularly perturbed parabolic equations consisting of linear as well as non-linear has been solved. Three numerical examples are presented to show the efficiency and effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

Numerous image formulae for a diversity of polynomials and functions subjected to a variety of fractional integrals and derivatives have been given. In this paper, we aimto construct image formulae for the product of incomplete H-functions and a general class of polynomials under the Katugampola fractional integral and derivative operators . We also provide some particular instances of our main findings in corollaries, among many others [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]

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]

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]

The Covid-19 outbreak hit us as a serious health crisis with vaccination to be seen as the only way out of it. And media can play the role of an advocate to fight against this epidemic by spreading important awareness regarding various protocols and vaccination strategies. Since breakthrough infections are becoming highly common, a two dose vaccine regime may be the need of the hour even for individuals with a pre-existing illness to build better immunity. Thus in this paper, our aim is to analyse a mathematical model with two dose vaccination strategy in the presence of media and breakthrough infections. An SIV1V2R model is formulated and the dynamical analysis is done. The basic reproduction number is obtained and the local stability analysis of both the disease-free and endemic equilibrium point is discussed based on reproduction number. The global stability of the endemic equilibrium point is done by graph theoretic approach. Finally, the numerical validation of the analytic solution is done using MATLAB using the real data of India for some important parameters to address a few vital questions which involves the role of media on the vaccination strategy. And sensitive model parameters effecting the basic reproduction number and endemic equilibrium points are identified using sensitivity analysis techniques like PRCC(partial rank correlation coefficient). Thus, the outcomes demonstrated the trend a two-dose vaccine model can follow and how the effect of media can help bring down the infections. This model provides support that two dose vaccination against COVID-19 with media presence for awareness is highly effective in controlling this epidemic. [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 estimate 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]

In this paper, two-parameter singularly perturbed parabolic equations are examined by two level method using non-polynomial spline. We have used non-polynomial quadratic spline in space and finite difference discretization in time. Stability analysis is carried out. The approximate solution is shown to converge point-wise to the true solution. Numerical solution of singularly perturbed parabolic equations consisting of linear as well as non-linear has been solved. Three numerical examples are presented to show the efficiency and effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

Recently, the idea of φ-fixed point and the elementary results on φ-fixed points were first investigated by Jleli et al. [Jleli M, Samet B, Vetro C (2014) Fixed point theory in partial metric spaces via φ-fixed point's concept in metric spaces. Journal of Inequalities and Applications, 2014(1):1-9.]. Based on this work, Karapinar et al. [Karapinar E, O'Regan D, Samet B (2015) On the existence of fixed points that belong to the zero set of a certain function. Fixed Point Theory and Applications, 2015(1):1-14.] established the new φ-fixed point results, which can be reduced to the famous fixed point result of Boyd and Wong in 1969. However, the main result of Karapinar et al. does not cover the φ-fixed point results of Jleli et al. This paper aims to fulfill this gap by proving φ-fixed point results covering several φ-fixed point results and fixed point results. [ABSTRACT FROM AUTHOR]

Numerous image formulae for a diversity of polynomials and functions subjected to a variety of fractional integrals and derivatives have been given. In this paper, we aimto construct image formulae for the product of incomplete H-functions and a general class of polynomials under the Katugampola fractional integral and derivative operators . We also provide some particular instances of our main findings in corollaries, among many others. [ABSTRACT FROM AUTHOR]