Browsing by Author "Muthaiah, Subramanian"

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Citation - WoS: 39
Citation - Scopus: 43
Existence and Hyers-Ulam Type Stability Results for Nonlinear Coupled System of Caputo-Hadamard Type Fractional Differential Equations
(Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Thangaraj, Nandha Gopal; Muthaiah, Subramanian
This paper aims to present the existence, uniqueness, and Hyers-Ulam stability of the coupled system of nonlinear fractional differential equations (FDEs) with multipoint and nonlocal integral boundary conditions. The fractional derivative of the Caputo-Hadamard type is used to formulate the FDEs, and the fractional integrals described in the boundary conditions are due to Hadamard. The consequence of existence is obtained employing the alternative of Leray-Schauder, and Krasnoselskii's, whereas the uniqueness result, is based on the principle of Banach contraction mapping. We examine the stability of the solutions involved in the Hyers-Ulam type. A few examples are presented as an application to illustrate the main results. Finally, it addresses some variants of the problem.
Citation - WoS: 13
Citation - Scopus: 16
Existence of Solutions for Nonlinear Fractional Differential Equations and Inclusions Depending on Lower-Order Fractional Derivatives
(Mdpi, 2020) Baleanu, Dumitru; Muthaiah, Subramanian
This article deals with the solutions of the existence and uniqueness for a new class of boundary value problems (BVPs) involving nonlinear fractional differential equations (FDEs), inclusions, and boundary conditions involving the generalized fractional integral. The nonlinearity relies on the unknown function and its fractional derivatives in the lower order. We use fixed-point theorems with single-valued and multi-valued maps to obtain the desired results, through the support of illustrations, the main results are well explained. We also address some variants of the problem.
Citation - WoS: 5
Citation - Scopus: 4
Existence Results for Coupled Differential Equations of Non-Integer Order With Riemann-Liouville, Erdelyi-Kober Integral Conditions
(Amer inst Mathematical Sciences-aims, 2021) Hemalatha, S.; Duraisamy, P.; Pandiyan, P.; Muthaiah, Subramanian; Baleanu, Dumitru
This paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdelyi-Kober and Riemann-Liouville fractional integral boundary conditions. The existence of the solution for the coupled system by adopting the Leray-Schauder alternative. The uniqueness of solution for the problem can be found using Banach fixed point theorem. In order to verify the proposed criterion, some numerical examples are also discussed.