Abstract
This manuscript is concerned with the approximate controllability problem of Hilfer fractional stochastic differential system (HFSDS) with Rosenblatt process and Poisson jumps. We derive the main results in stochastic settings by employing analytic resolvent operators, fractional calculus and fixed point theory. Further, we express the theoretical result with an example.
Funding source: Science and Engineering Research Board
Award Identifier / Grant number: MTR/2017/001011
Funding source: University Grants Commission
Award Identifier / Grant number: F. 510/7/DSA-1/2015 (SAP-I)
Acknowledgment
This work is supported partially by Mathematical Research Impact Centric Support, Department of Science and Technology – Science and Engineering Research Board, New Delhi, India, File No. MTR/2017/001011 and supported partially by University Grants Commission – Special Assistance Programme (Department of Special Assistance – I), New Delhi, India, File No. F. 510/7/DSA-1/2015 (SAP-I).
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Disclosure statement: The authors have no conflict of interest regarding this work.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- ANFIS based system identification of underactuated systems
- The dynamical behavior of mixed type lump solutions on the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation
- A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation
- Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation
- A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations
- Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations
- Integrodifference master equation describing actively growing blood vessels in angiogenesis
- On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product Lp and weighted Lp spaces
- Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps
- Lie symmetries and singularity analysis for generalized shallow-water equations
- Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system
- Nonlinear wave equation in an inhomogeneous medium from non-standard singular Lagrangians functional with two occurrences of integrals
- Lie symmetry analysis and similarity solutions for the Jimbo – Miwa equation and generalisations
- The barotropic Rossby waves with topography on the earth’s δ-surface
- Synchronization control between discrete uncertain networks with different topologies
- Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions
- Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays
- A parallel hybrid implementation of the 2D acoustic wave equation
- Approximate controllability of fractional stochastic evolution equations with nonlocal conditions
- Fractional (3+1)-dim Jimbo Miwa system: invariance properties, exact solutions, solitary pattern solutions and conservation laws
- Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber
Articles in the same Issue
- Frontmatter
- Original Research Articles
- ANFIS based system identification of underactuated systems
- The dynamical behavior of mixed type lump solutions on the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation
- A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation
- Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation
- A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations
- Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations
- Integrodifference master equation describing actively growing blood vessels in angiogenesis
- On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product Lp and weighted Lp spaces
- Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps
- Lie symmetries and singularity analysis for generalized shallow-water equations
- Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system
- Nonlinear wave equation in an inhomogeneous medium from non-standard singular Lagrangians functional with two occurrences of integrals
- Lie symmetry analysis and similarity solutions for the Jimbo – Miwa equation and generalisations
- The barotropic Rossby waves with topography on the earth’s δ-surface
- Synchronization control between discrete uncertain networks with different topologies
- Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions
- Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays
- A parallel hybrid implementation of the 2D acoustic wave equation
- Approximate controllability of fractional stochastic evolution equations with nonlocal conditions
- Fractional (3+1)-dim Jimbo Miwa system: invariance properties, exact solutions, solitary pattern solutions and conservation laws
- Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber