Research

My research primarily focuses on the Qualitative study of inverse problems for evolution equations and inclusions on abstract spaces, such as the existence, uniqueness, and stability of solutions. Some of the research keywords of my interests are:

• Inverse Problems

• Evolution Equations                                                                               

• Optimal Control Theory 

• Differential Inclusions

• Functional Differential Equations 

• Impulsive Differential Equations 

Publications:

1. S. Ruhil and M. Malik, "Inverse problem for the Atangana–Baleanu fractional differential equation," Journal of Inverse and Ill-posed Problems, vol. 31, no. 5, 2023, pp. 763-779. https://doi.org/10.1515/jiip-2022-0025 

2. M. Malik and S. Ruhil,  "Inverse problem for an abstract neutral differential equation of Sobolev type," Results in Control and Optimization, 11 (2023): 100235.  https://doi.org/10.1016/j.rico.2023.100235 

3. M. Malik, S. Ruhil and R. Dhayal. "An Investigation of an Inverse Problem for Second-Order Abstract Differential Equation," Indian Journal of Pure and Applied Mathematics, 2023, 56(24): 512-525. https://doi.org/10.1007/s13226-023-00498-9 

4. S. Ruhil and M. Malik, "Inverse Problem for  Abstract Delay Differential Equation with Impulsive Effects," Evolution Equations and Control Theory, 2024, 13(3): 751-766. https://doi.org/10.3934/eect.2024004

5. S. Ruhil and M. Malik, "Approximation Results for Abstract Inverse Problem in Impulsive Differential Equation," Discrete & Continuous Dynamical Systems - Series S, 2024. 10.3934/dcdss.2024161 

6. S. Ruhil and M. Malik, "Parameter Identification Problem for the Abstract State-Dependent Delay Differential Equation," Mathematical Methods in the Applied Sciences, 2025. 10.1002/mma.10811 

7. S. Ruhil, M. Malik, K. S. Nisar, F. Al Shammarri, "Approximation of Inverse Problems for Fractional Differential Equations in Abstract Spaces," Alexandria Engineering Journal, 2025, 121(24): 529-538. https://doi.org/10.1016/j.aej.2025.02.079 

8. S. Ruhil and M. Malik, "Inverse Problem for an Abstract Differential Equation with Non-Instantaneous Impulses," The Rocky Mountain Journal of Mathematics, 2025, 55(2): 517-531. http://dx.doi.org/10.1216/rmj.2025.55.517

9.  S. Ruhil and M. Malik, "Parameter Identification Problem for Semilinear Abstract Degenerate Delay Differential Equation," Qualitative Theory of Dynamical Systems, 2025, 24(177). https://doi.org/10.1007/s12346-025-01334-7

10.  S. Ruhil and M. Malik, "Results on Inverse Problem for Abstract Semilinear Differential Inclusions,'' Journal of Inverse and Ill-posed Problems, 2025. https://doi.org/10.1515/jiip-2024-0045

11. S. Ruhil and M. Malik, "Parameter Identification Problem for Abstract Functional Differential Inclusions,'' Complex Analysis and Operator Theory, 2026. 20(3), 89. https://doi.org/10.1007/s11785-026-01943-3 

Projects:

• September 2021-August 2022, "Inverse problems for abstract differential equations and applications in fluid dynamics," (Indian Institute of Technology Mandi, Himachal Pradesh, India). (Project Investigator: Prof. Muslim Malik).

• June 2019-July 2020,  "The study of Dilation Theory," (Indian Institute of Technology Mandi, Himachal Pradesh, India). (Project Investigator: Dr. Kalpesh Haria).