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Vaibhav Mehandiratta

Bio: Vaibhav Mehandiratta is an academic researcher from Indian Institute of Technology Delhi. The author has contributed to research in topics: Fractional calculus & Metric (mathematics). The author has an hindex of 5, co-authored 8 publications receiving 68 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, a nonlinear Caputo fractional boundary value problem on a star graph is studied, and the existence and uniqueness results by fixed point theory are established by using Banach's contraction principle and Schaefer's fixed point theorem.

42 citations

Journal ArticleDOI
TL;DR: In this article, the adjoint state and the optimality system are derived for fractional optimal control problem (FOCP) by using the Lagrange multiplier method, then, the existence and uniqueness of solution of the adjointed equation is proved by means of the Banach contraction principle.
Abstract: In this paper, we study optimal control problems for nonlinear fractional order boundary value problems on a star graph, where the fractional derivative is described in the Caputo sense. The adjoint state and the optimality system are derived for fractional optimal control problem (FOCP) by using the Lagrange multiplier method. Then, the existence and uniqueness of solution of the adjoint equation is proved by means of the Banach contraction principle. We also present a numerical method to find the approximate solution of the resulting optimality system. In the proposed method, the \begin{document}$ L2 $\end{document} scheme and the Grunwald-Letnikov formula is used for the approximation of the Caputo fractional derivative and the right Riemann-Liouville fractional derivative, respectively, which converts the optimality system into a system of linear algebraic equations. Two examples are provided to demonstrate the feasibility of the numerical method.

34 citations

Journal ArticleDOI
TL;DR: A neural network problem modeled by a system of nonlinear fractional differential equations is solved using the proposed method and the numerical results show that the proposed numerical approach is efficient.

23 citations

Journal ArticleDOI
TL;DR: In this paper, an unconditionally stable numerical scheme based on finite difference for the approximation of time-fractional diffusion equation on a metric star graph is proposed, and the convergence and stability of the difference scheme has been proved by means of energy method.

19 citations

Journal ArticleDOI
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...
Abstract: We study 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...

17 citations


Cited by
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Journal ArticleDOI
TL;DR: In this article, the adjoint state and the optimality system are derived for fractional optimal control problem (FOCP) by using the Lagrange multiplier method, then, the existence and uniqueness of solution of the adjointed equation is proved by means of the Banach contraction principle.
Abstract: In this paper, we study optimal control problems for nonlinear fractional order boundary value problems on a star graph, where the fractional derivative is described in the Caputo sense. The adjoint state and the optimality system are derived for fractional optimal control problem (FOCP) by using the Lagrange multiplier method. Then, the existence and uniqueness of solution of the adjoint equation is proved by means of the Banach contraction principle. We also present a numerical method to find the approximate solution of the resulting optimality system. In the proposed method, the \begin{document}$ L2 $\end{document} scheme and the Grunwald-Letnikov formula is used for the approximation of the Caputo fractional derivative and the right Riemann-Liouville fractional derivative, respectively, which converts the optimality system into a system of linear algebraic equations. Two examples are provided to demonstrate the feasibility of the numerical method.

34 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigate the existence results for a novel modeling of the fractional multi-term boundary value problems on each edge of the graph representation of the Glucose molecule.

29 citations

Journal ArticleDOI
TL;DR: This work investigates the existence of solutions for some fractional boundary value problems on the ethane graph and defines fractional differential equations on each edge of this graph.
Abstract: A few researchers have studied fractional differential equations on star graphs. They use star graphs because their method needs a common point which has edges with other nodes while other nodes have no edges between themselves. It is natural that we feel that this method is incomplete. Our aim is extending the method on more generalized graphs. In this work, we investigate the existence of solutions for some fractional boundary value problems on the ethane graph. In this way, we consider a graph with labeled vertices by 0 or 1, inspired by a graph representation of the chemical compound of ethane, and define fractional differential equations on each edge of this graph. Also, we provide an example to illustrate our last main result.

27 citations