10. An analysis of nonlinear integro-differential equations with four-point nonlocal boundary value problem using Ψ-Caputo fractional derivatives (2025).
Poovarasan R., Mohammad Esmael Samei, V. Govindaraj.
This study analyzes a fractional boundary value problem involving nonlinear differential equations. The existence of solutions is established using a fixed-point theorem due to D. O’Regan, while uniqueness is ensured via the contraction mapping principle in Banach spaces. To support the analytical findings, numerical examples are presented, illustrating the effectiveness and reliability of the proposed framework.
9. Advanced analysis of Ψ-Caputo fractional derivative in multiple-point boundary value problems (2025).
Poovarasan R., V. Govindaraj.
This study analyzes a fractional boundary value problem involving nonlinear differential equations. The existence of solutions is established using a fixed-point theorem due to D. O’Regan, while uniqueness is ensured via the contraction mapping principle in Banach spaces. To support the analytical findings, numerical examples are presented, illustrating the effectiveness and reliability of the proposed framework.
8. Existence of Solutions for a Coupled System of ψ-Caputo Fractional Differential Equations With Integral Boundary Conditions (2025).
Poovarasan R., V. Govindaraj.
This research contributes to coupled nonlocal boundary conditions with integral constraints, introducing a novel problem within fractional calculus and nonlinear dynamics. Our main contributions include proving the existence of solutions obtained via Leray–Schauder's alternative and establishing uniqueness via the contraction mapping principle.
Poovarasan R., Mohammad Esmael Samei, V. Govindaraj.
This research contributes to advancing the analytical understanding and practical applications of fractional calculus in modeling and analyzing complex systems governed by nonlinear dynamics and integral constraints.
Poovarasan R., Thabet Abdeljawad., V. Govindaraj.
This study investigates the analysis of the existence, uniqueness, and stability of solutions for a Ψ-Caputo three-point nonlinear fractional boundary value problem using the Banach contraction principle and Sadovskii's fixed point theorem.
5. Study of three-point impulsive boundary value problems governed by ψ-Caputo fractional derivative (2024).
Poovarasan R., Mohammad Esmael Samei, V. Govindaraj.
In this study, we investigate the existence and uniqueness of solutions for specific type of three-point boundary value problems. These problems focus on nonlinear impulsive fractional differential equations, which pose a challenge in finding their solutions.
Poovarasan R., J F Gómez-Aguilar, V. Govindaraj.
This study uses fixed point theory and the Banach contraction principle to prove the existence, uniqueness, and stability of solutions to boundary value problems involving a Ψ-Caputo-type fractional differential equation.
Poovarasan R., Pushpendra Kumar.,V. Govindaraj, Marina Murillo-Arcila.
In this article, we use coupled boundary conditions on a nonlinear system with ψ-Caputo fractional derivatives to derive new conclusions on the solution’s existence, uniqueness, and stability.
Poovarasan R., Pushpendra Kumar., Kottakkaran Sooppy Nisar., V. Govindaraj.
In this article, we derive some novel results of the existence, uniqueness, and stability of the solution of generalized Caputo-type fractional boundary value problems (FBVPs).
1. Some novel analyses of the Caputo-type singular three-point fractional boundary value problems (2023).
Poovarasan R., Pushpendra Kumar., Sivalingam S.M., V. Govindaraj.
In this article, we consider singular three-point second-order boundary value problems in the sense of the Caputo fractional derivatives. We derive some novel results on the existence of a unique solution for the proposed problems.