On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative

Sutar, Sagar T.; Kucche, Kishor D.

doi:10.1016/j.chaos.2020.110557

Cited by 24 publications

(13 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Freshly, some authors have studied di erent characteristics of Hybrid FDEs including the existence of solutions (see [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]), and some go further and studied Hyers-Ulam stability for FDEs by di erent mathematical theories; see [28][29][30] for some details.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Coupled System of Caputo–Hadamard Fractional Hybrid Differential Equations with Three-Point Boundary Conditions

Arab

Awadalla

2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This article presents a study of the existence and uniqueness of solutions for a system of hybrid fractional differential equations involving fractional derivatives of the Caputo-Hadamard type with three-point hybrid boundary conditions. In addition to this, the “Hyres–Ulam” stability of the solutions for this type of equation is verified, and finally a numerical example was presented to support our theoretical results.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Some researchers focus on having solutions to a system of equations only (see [8,25,26,29,31]). However, others went deeper in their research beyond the issue of verifying the issue of the existence of a solution to such equations and studied the issue of the stability of these solutions (see [21,[35][36][37]).…”

Section: Introductionmentioning

confidence: 99%

A Coupled System of Caputo–Hadamard Fractional Hybrid Differential Equations with Three-Point Boundary Conditions

Arab

Awadalla

2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…For instance, Baleanu [2] applied Caputo fractional-order hybrid di erential equations to analyze a thermostat model. Other contributions on fractional-order hybrid di erential equations involving the Hadamard derivative [3], Riemann derivative [4], Hilfer derivative [5], and Atangana derivative [6,7] (ABC).…”

Section: Introductionmentioning

confidence: 99%

Existence and Stability for a Coupled Hybrid System of Fractional Differential Equations with Atangana–Baleanu–Caputo Derivative

Zhao

Jiang

2022

Journal of Mathematics

View full text Add to dashboard Cite

The aim of this article is to investigate a coupled hybrid system of fractional differential equations with the Atangana–Baleanu–Caputo derivative which contains a Mittag–Leffler kernel function in its kernel. We firstly apply the Dhage fixed point principle to obtain the existence of mild solutions. Then, we study the Ulam–Hyers stability of the introduced fractional coupled hybrid system. Finally, an example is presented to exhibit the validity of our results.

show abstract

“…For FDEs, we refer to [19,20]. Freshly, some authors have studied different characteristics of hybrid FDEs including the existence of solutions, see for some detail [21][22][23][24][25][26][27][28][29], and some go further and studied Hyers-Ulam stability for FDEs by different mathematical theories, see for some detail [26].…”

Section: Introductionmentioning

confidence: 99%

On System of Mixed Fractional Hybrid Differential Equations

Awadalla

Mahmudov

2022

Journal of Function Spaces

View full text Add to dashboard Cite

In this article, we find the necessary conditions for the existence and uniqueness of solutions to a system of hybrid equations that contain mixed fractional derivatives (Caputo and Riemann-Liouville). We also verify the stability of these solutions using the Ulam-Hyers (U-H) technique. Finally, this study ends with applied examples that show how to proceed and verify the conditions of our theoretical results.

show abstract

On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative

Cited by 24 publications

References 23 publications

A Coupled System of Caputo–Hadamard Fractional Hybrid Differential Equations with Three-Point Boundary Conditions

A Coupled System of Caputo–Hadamard Fractional Hybrid Differential Equations with Three-Point Boundary Conditions

Existence and Stability for a Coupled Hybrid System of Fractional Differential Equations with Atangana–Baleanu–Caputo Derivative

On System of Mixed Fractional Hybrid Differential Equations

Contact Info

Product

Resources

About