On system of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order

Subramanian, Muthaiah; Manigandan, Murugesan; Tunç, Cemil; Gopal, Thangaraj Nandha; Alzabut, Jehad

doi:10.1080/16583655.2021.2010984

Cited by 30 publications

(11 citation statements)

References 52 publications

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“…At the same time, the existence analysis, uniqueness analysis, stability analysis of solutions in fractional differential equation become an important research direction. Many scholars have studied them in recent years, and readers can refer to the literature [3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Non-Negative Solution to a Coupled Fractional q-Difference System with Mixed q-Derivative via Mixed Monotone Operator Method

Meng

et al. 2023

Mathematics

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In this paper, we study a nonlinear Riemann-Liouville fractional a q-difference system with multi-strip and multi-point mixed boundary conditions under the Caputo fractional q-derivative, where the nonlinear terms contain two coupled unknown functions and their fractional derivatives. Using the fixed point theorem for mixed monotone operators, we constructe iteration functions for arbitrary initial value and acquire the existence and uniqueness of extremal solutions. Moreover, a related example is given to illustrate our research results.

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Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Non-Negative Solution to a Coupled Fractional q-Difference System with Mixed q-Derivative via Mixed Monotone Operator Method

Meng

et al. 2023

Mathematics

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“…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%

“…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

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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.

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“…e authors proved the existence and uniqueness results with the aid of standard xed point to obtain their results. Recently, Subramanian et al [29] studied the existence of positive solutions for nonlinear coupled system of fractional differential equations complemented with boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Existence and Stability Results for Caputo-Type Sequential Fractional Differential Equations with New Kind of Boundary Conditions

Awadalla

Manigandan

2022

Mathematical Problems in Engineering

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In this paper, we present the existence and the stability results for a nonlinear coupled system of sequential fractional differential equations supplemented with a new kind of coupled boundary conditions. Existence and uniqueness results are established by using Schaefer’s fixed point theorem and Banach’s contraction mapping principle. We examine the stability of the solutions involved in the Hyers–Ulam type. A few examples are presented to illustrate the main results.

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On system of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order

Cited by 30 publications

References 52 publications

Existence and Uniqueness of Non-Negative Solution to a Coupled Fractional q-Difference System with Mixed q-Derivative via Mixed Monotone Operator Method

Existence and Uniqueness of Non-Negative Solution to a Coupled Fractional q-Difference System with Mixed q-Derivative via Mixed Monotone Operator Method

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

Existence and Stability Results for Caputo-Type Sequential Fractional Differential Equations with New Kind of Boundary Conditions

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