Journal ArticleDOI
Collocation method for solving nonlinear fractional optimal control problems by using Hermite scaling function with error estimates
Nitin Kumar,Mani Mehra +1 more
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This article is published in Optimal Control Applications & Methods.The article was published on 2021-03-01. It has received 26 citations till now. The article focuses on the topics: Collocation method & Hermite polynomials.read more
Citations
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Journal ArticleDOI
Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost
Nitin Kumar,Mani Mehra +1 more
Journal ArticleDOI
Wavelet collocation method based on Legendre polynomials and its application in solving the stochastic fractional integro-differential equations
Abhishek Singh,Mani Mehra +1 more
TL;DR: The numerical method presented here is a wavelet collocation method based on Legendre polynomials, and their deterministic and stochastic operational matrix of integration, which is used to convert the Stochastic fractional integro-differential equation to a linear system of algebraic equations.
Journal ArticleDOI
The formally second-order BDF ADI difference/compact difference scheme for the nonlocal evolution problem in three-dimensional space
TL;DR: In this paper, two kinds of alternating direction implicit (ADI) schemes for the parabolic-type three-dimensional evolution equation with a weakly singular kernel were proposed, where the second-order backward differentiation formula (BDF2) and the secondorder convolution quadrature (CQ) technique were applied to discretize the time derivative and the Riemann-Liouville integral, respectively.
Journal ArticleDOI
The formally second-order BDF ADI difference/compact difference scheme for the nonlocal evolution problem in three-dimensional space
TL;DR: In this article , two kinds of alternating direction implicit (ADI) schemes for the parabolic-type three-dimensional evolution equation with a weakly singular kernel were proposed, where the second-order backward differentiation formula (BDF2) and the secondorder convolution quadrature (CQ) technique were applied to discretize the time derivative and the Riemann-Liouville integral, respectively.
Journal ArticleDOI
Optimal Control Problems Driven by Time-Fractional Diffusion Equations on Metric Graphs: Optimality System and Finite Difference Approximation
TL;DR: In this article, the authors studied optimal control problems for time-fractional diffusion equations on metric graphs, where the fractional derivative is considered in the Caputo sense, using eigenfunction expansions for the...
References
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Book
Applied Optimal Control: Optimization, Estimation, and Control
TL;DR: This best-selling text focuses on the analysis and design of complicated dynamics systems and is recommended by engineers, applied mathematicians, and undergraduates.
BookDOI
Fractals and fractional calculus in continuum mechanics
TL;DR: Panagiotopoulos, O.K.Carpinteri, B. Chiaia, R. Gorenflo, F. Mainardi, and R. Lenormand as mentioned in this paper.
Journal ArticleDOI
A new dissipation model based on memory mechanism
TL;DR: The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.
Journal ArticleDOI
Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids
Journal ArticleDOI
A General Formulation and Solution Scheme for Fractional Optimal Control Problems
TL;DR: In this article, a general formulation and a solution scheme for a class of Fractional Optimal Control Problems (FOCPs) for those systems are presented, where the performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of FDEs.
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Fourth order compact scheme for space fractional advection–diffusion reaction equations with variable coefficients
Kuldip Singh Patel,Mani Mehra +1 more