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In this work we use a decomposition method which is called differential transform method (DTM) to obtain the numerical or analytical solutions of fuzzy differential equations. The DTM has been applied to many nonlinear differential equations of integer order as well as fractional orders. Here by considering strongly generalized differentiable of fuzzy differential equations we obtain all possible...
The present study discloses the three dimensional flow and heat transfer of water-based nanofluid tempted by an extendable surface subject to the effects of couple stress and thermal radiation. Fe$$_{3}$$ 3 O$$_{4}$$ 4 nanoparticles in water-based couple stress nanofluid are considered. The consequence of nonlinear thermal radiation is sought. Using appropriate similarity transformations, governing...
In this paper, effect of thermal radiation on the unsteady 3-dimensional flow of nanofluid (Cu-water) past a vertical flat surface is examined in rotating frame of reference. The surface is assumed to be executing harmonic oscillations about a constant mean velocity. By the use of appropriate transformations, governing equations and boundary conditions are obtained in dimensionless form. Due to non-availability...
This paper deals with the vibration and buckling analysis of skew functionally graded material (FGM) plates. A finite element mathematical model is developed based on higher order shear deformation theory. The model is based on an eight noded isoparametric element with seven degrees of freedom per node. The material properties are graded along thickness direction obeying simple power-law distribution...
In this paper we apply an empirically generated relation to investigate strain hardening of nonlinear polymeric jets, such as those due to polymeric melts like Boger fluids, which can be generated by the forcespinning process (FS). We apply scaling and perturbation analyses to determine a simplified modeling FS system for the nonlinear fiber jets and calculate numerically the expressions for the nonlinear...
The magnetohydrodynamics boundary layer flows with Naviers’ slip condition are mathematically modelled into highly nonlinear partial differential equations which are then transformed into highly nonlinear ordinary differential equations. The similarity solutions are obtained and are analysed means of differential transform method and with an application of Pade approximants to the highly nonlinear...
Das et al. (Comput Math Appl 60(7):1973–1985, 2010) proposed a production inventory model for a deteriorating item under permissible delay in payments assuming that the demand is stock dependent. In the production inventory model, the production rate is partially constant and dependent upon on both on-hand inventory and demand. The production inventory model assumes that the supplier gives a price...
This paper is concern with the study of steady magnetohydrodynamic radiative dissipative boundary layer flow of a reactive Casson nanofluid over a permeable vertical nonlinear stretching/shrinking surface. We have incorporated the combined effects of viscous and Ohmic dissipation, thermophoresis and Brownian motion on heat and mass transfer in Casson nanofluid in the presence of chemical reaction...
In this paper, we derive an explicit expression of $$(P+Q)^{d}$$ (P+Q)d of two matrices P and Q, in terms of P, Q, $$P^d$$ Pd and $$Q^{d}$$ Qd , assuming some conditions. And we also obtain representations for the Drazin inverse of complex block matrix $$\left( \begin{array}{ccc} A &{} B \\ C &{} D \end{array} \right) $$ ABCD (A and D are square) under some conditions. Finally, numerical...
Theoretical analysis of entropy generation in three dimensional boundary layer flow over a bidirectional exponentially stretching surface in the presence of viscous dissipation is performed. By taking suitable similarity transformations governing partial differential equations are reduced to ordinary differential equations. Expressions for entropy generation and Bejan number are also obtained via...
The paper outlines a numerical method called boundary element method (BEM) which is employed to study heat transfer through the walls of arbitrary shaped heat exchanger tubes having arbitrary shaped holes. The method is implemented for two different cases to obtain the approximate solution of the two dimensional Laplace equation. For both the cases, the inner surfaces are maintained at a constant...
This article continues the research on line search techniques for fuzzy optimization problems. Previously, in Ghosh and Chakraborty (Int J Appl Comput Math 3(2):527–547, 2017), a quadratic interpolation technique for fuzzy optimization problem was studied. In this article, we propose a cubic interpolation technique. For the optimality concept, a partial ordering of fuzzy numbers is used. In order...
In this paper, we study a class of singularly perturbed Riccati equation with fractional order. We divide the problem into three problems. The first problem is the reduced problem when $$\epsilon =0$$ ϵ=0 . The second and third problems are fractional Riccati problem. The results show that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. Numerical...
In this paper, a new stage structured prey–predator model with Monod–Haldane functional response is proposed and the stages for predator have been considered. The proposed mathematical model consists of three nonlinear delay differential equations to describe the interaction among prey, immature predator and mature predator populations. Two time delays viz. feedback delay and gestation delay have...
An inequality involving the q-gamma and q-trigamma functions is derived and proved for all real number $$q>0$$ q>0 . This inequality provides new bounds for the q-gamma function in terms of the q-trigamma function.
The quaternions play a crucial role in various research areas such as computer graphic, integrated navigation systems, color image processing, signal processing, quantum physics etc. Consider the quaternion least-squares problem $$\begin{aligned} \min \,\,\left\| {\sum \limits _{j = 1}^q { {\left( {{A_{ij}}{X_j}{B_{ij}} + {C_{ij}}X_j^{\eta H}{D_{ij}} - {E_i}} \right) } } } \right\| ,\qquad i=1,2,\ldots...
With respect to wide range of applications of stochstic partial differential equation (SPDE) and high ability of meshless methods to solve complicated problems, in this paper, an efficient numerical method for the time fractional SPDE, formulated with Caputo’s fractional derivative, based on meshless methods is presented. This article presents a meshless method based on the radial basis functions...
The object of this paper is to establish the left and right-sided generalized fractional calculus formulas involving the product of generalized Mittag-Leffler function and general class of multivariable polynomials. The results obtained in this paper are presented in terms of Wright generalized hypergeometric function. Further, we point out also their relevance.
In this paper, we study the existence and uniqueness of mild solutions for Sobolev type fractional impulsive differential systems with fractional order nonlocal conditions by applying monotone iterative technique coupled with the method of lower and upper solutions. The sufficient conditions are obtained by measure of noncompactness and generalized Gronwall inequality. Finally, an application is given...
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