Initial and Boundary Value Problems for Fuzzy Differential Equations

Murty, M. S. N.; Kumar, G. Suresh

doi:10.1515/dema-2007-0409

Cited by 5 publications

(3 citation statements)

References 11 publications

(10 reference statements)

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“…In relation with degenerated ordinary differential equation systems, some new findings are reported in [25]. The existence of some three-point BVPs determined by non-linear DEs of order three is assessed in [26] by means of Green functions. In [27], for a class of ordinary differential equations of order two, a method is presented in order to find the Green functions for three-point BVPs.…”

Section: Introductionmentioning

confidence: 99%

Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

2023

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It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support. Determination of the critical load for these beams leads to three point boundary value problems (BVPs) associated with homogeneous boundary conditions—the mentioned BVPs constitute three eigenvalue problems. They are solved by using a novel solution strategy based on the Green functions that belong to these BVPs: the eigenvalue problems established for the critical load are transformed into eigenvalue problems governed by homogeneous Fredholm integral equations with kernels that can be given in closed forms provided that the Green function of each BVP is known. Then the eigenvalue problems governed by the Fredholm integral equations can be manipulated into algebraic eigenvalue problems solved numerically by using effective algorithms. It is an advantage of the way we attack these problems that the formalism established and the results obtained remain valid for homogeneous beams as well. The numerical results for the critical forces can be applied to solve some stability problems in the engineering practice.

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Section: Introductionmentioning

confidence: 99%

Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

2023

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“…Georgiou et al [13] established the existence and uniqueness of solutions of Cauchy problems for FDEs of second order and FIVPs of higher order in [14] under H-differentiability. Further, Murty and Suresh Kumar [17] obtained the existence and uniqueness criteria for fuzzy initial and boundary value problems. Furthermore, Allahviranloo et al [3] studied the existence and uniqueness of solutions of second-order FDEs under SGH-differentiability.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solutions for fuzzy initial value problems under granular differentiability

Soma¹,

Grande²,

Agarwal³

et al. 2023

J. Math. Computer Sci.

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In this paper, we introduce the notion of second and higher-order granular differentiability for fuzzy number-valued functions. A weighted granular metric is defined for continuously granular differentiable mappings and proves that it is a complete metric space. Fuzzy initial value problems are investigated for second and higher-order fuzzy differential equations under granular differentiability. Sufficient conditions are established for the existence and uniqueness of solutions for the fuzzy initial value problems. An algorithm is developed to determine the solution to the fuzzy initial value problem under granular differentiability. Moreover, examples are presented to verify our theoretical results and algorithm.

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“…In Bede and Gal (2005), the author introduced the notion of strongly generalized differentiability of fuzzy-number-valued functions. Fuzzy set theory and its applications have been extensively developed by many authors (Kaleva 1987;Lakshmikantham and Mohapatra 2003;Murthy and Suresh-Kumar 2006, 2007, 2008aMurthy et al 2013).…”

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confidence: 99%

Generalized differentiability and integrability for fuzzy set-valued functions on time scales

Vasavi

Kumar

Murty³

2014

Soft Comput

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Initial and Boundary Value Problems for Fuzzy Differential Equations

Abstract: Abstract. This paper deals with the study of existence and uniqueness criteria for initial and boundary value problems associated with fuzzy differential equations of first and second order with the help of a modified Lipschitz condition.

Cited by 5 publications

References 11 publications

Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

Existence and uniqueness of solutions for fuzzy initial value problems under granular differentiability

Generalized differentiability and integrability for fuzzy set-valued functions on time scales

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