On Caputo-Hadamard Type Fractional Differential Equations with Nonlocal Discrete Boundary Conditions

Manigandan, Murugesan; Subramanian, Muthaiah; Duraisamy, Palanisamy; Gopal, Thangaraj Nandha

doi:10.5890/dnc.2021.06.002

Cited by 5 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerous phenomena in various disciplines of engineering and science are described by fractional differential equations, ranging from theoretical physics to astrophysics and astronomy, from dynamical chaos to signal processing, and from signal processing to networking. For current and wide-ranging analyses of fractional derivatives and their applications, we recommend certain monographs [1][2][3][4] and recently mentioned papers [5][6][7][8][9][10][11][12][13][14]. The majority of research on FDEs is based on fractional derivatives of the Riemann-Liouville and Caputo types (see [5,8,11,12,15]).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Existence and Stability Results for a Tripled System of the Caputo Type with Multi-Point and Integral Boundary Conditions

et al. 2022

Self Cite

View full text Add to dashboard Cite

In this paper, we introduce and investigate the existence and stability of a tripled system of sequential fractional differential equations (SFDEs) with multi-point and integral boundary conditions. The existence and uniqueness of the solutions are established by the principle of Banach’s contraction and the alternative of Leray–Schauder. The stability of the Hyer–Ulam solutions are investigated. A few examples are provided to identify the major results.

show abstract

Section: Introductionmentioning

confidence: 99%

“…For current and wide-ranging analyses of fractional derivatives and their applications, we recommend certain monographs [1][2][3][4] and recently mentioned papers [5][6][7][8][9][10][11][12][13][14]. The majority of research on FDEs is based on fractional derivatives of the Riemann-Liouville and Caputo types (see [5,8,11,12,15]).…”

Section: Introductionmentioning

confidence: 99%

Existence and Stability Results for a Tripled System of the Caputo Type with Multi-Point and Integral Boundary Conditions

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…By using this operator, very few fractional models and problems were produced. Examples can be seen in [26][27][28][29]. However, the Hadamard fractional derivative (HFD) is the most frequently used [30].…”

Section: Introductionmentioning

confidence: 99%

Existence and H-U Stability of Solution for Coupled System of Fractional-Order with Integral Conditions Involving Caputo-Hadamard Derivatives, Hadamard Integrals

Awadalla

Subramanian

Manigandan

et al. 2022

Journal of Function Spaces

Self Cite

View full text Add to dashboard Cite

In this article, the primary focus of our study is to investigate the existence, uniqueness, and Ulam-Hyers stability results for coupled fractional differential equations of the Caputo-Hadamard type that are supplemented with Hadamard integral boundary conditions. We employ adequate conditions to achieve existence and uniqueness results for the presented problems by utilizing the Banach contraction principle and the Leray-Schauder fixed point theorem. We also show Ulam-Hyers stability using the standard functional analysis technique. Finally, examples are used to validate the results.

show abstract

A Novel Implementation of Mönch’s Fixed Point Theorem to a System of Nonlinear Hadamard Fractional Differential Equations

et al. 2022

View full text Add to dashboard Cite

In this article, we employed Mönch’s fixed point theorem to investigate the existence of solutions for a system of nonlinear Hadamard fractional differential equations and nonlocal non-conserved boundary conditions in terms of Hadamard integral. Followed by a study of the stability of this solution using the Ulam-Hyres technique. This study concludes with an applied numerical example that helps in understanding the theoretical results obtained.

show abstract

On Caputo-Hadamard Type Fractional Differential Equations with Nonlocal Discrete Boundary Conditions

Cited by 5 publications

References 0 publications

Existence and Stability Results for a Tripled System of the Caputo Type with Multi-Point and Integral Boundary Conditions

Existence and Stability Results for a Tripled System of the Caputo Type with Multi-Point and Integral Boundary Conditions

Existence and H-U Stability of Solution for Coupled System of Fractional-Order with Integral Conditions Involving Caputo-Hadamard Derivatives, Hadamard Integrals

A Novel Implementation of Mönch’s Fixed Point Theorem to a System of Nonlinear Hadamard Fractional Differential Equations

Contact Info

Product

Resources

About