Fractional Differential Equations Involving Hadamard Fractional Derivatives with Nonlocal Multi-point Boundary Conditions

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

doi:10.5890/dnc.2020.09.006

Cited by 10 publications

(3 citation statements)

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“…Te study of boundary value problems for equations with nonlinear fractional diferentials has a prominent and important role in the theory of fractional calculus and in the study of physical phenomena through the physical interpretation of boundary conditions. To pass quickly to the practical applications of fractional derivatives in various applied sciences, some valuable works in this feld can be found in [11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

Awadalla

Abuasbeh

Manigandan

et al. 2023

Journal of Mathematics

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In this article, we study the existence of the solution for the fractional differential equations of sequential type with nonlocal integral boundary conditions. The main results are established with the aid of Darbo’s fixed point theorem and Hausdorff’s measure of noncompactness method. The stability of the proposed fractional differential equation is also investigated via the Ulam–Hyer technique. In addition, an applied example that supports the theoretical results reached through this study is included.

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Section: Introductionmentioning

confidence: 99%

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

Awadalla

Abuasbeh

Manigandan

et al. 2023

Journal of Mathematics

Self Cite

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“…The challenge of studying the existence and uniqueness solution is the study of its stability. Ulam-Hyers stability (UHS) is the most important types of stability is used in this field ( see [4,10,17,27,28,44], [7,25], [19]) Su [43], studied the existence of solutions for a coupled system of fractional differential equations:…”

Section: Introductionmentioning

confidence: 99%

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

MURAD,

RAFEEQ,

IBRAHIM

et al. 2023

Preprint

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The solvability of a fractional differential equation depends on various factors such as the type of equation, the order of the fractional derivative, the domain and boundary conditions, and the properties of the solution sought. In this paper, The solution of a system of Caputo-Hadamard fractional differential equations (SCH) with integral boundary condition is investigated. The existence theorem of solutions is established by means of the Krasnoselskii and Schaefer’s fixed point theorem. Further, the uniqueness result is presented which is based on Banach’s contraction principle. Finally, the stability of the given system in Ulam-Hyers sense is applied. Examples are considered for the verification of theoretical works.

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“…, p located at an arbitrary position in the aperture (slit)-the region of the boundary off the strips. Examples of such boundary conditions include scattering by slits silicon strips detectors for scanned multi-slit X-ray imaging, acoustic impedance of baffled strips radiators, diffraction from an elastic knife-edge adjacent to a strip, sound fields of infinitely long strips, dielectric-loaded multiple slits in a conducting plane, lattice engineering [25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Hybrid Coupled System of ψ-Caputo Fractional Derivatives with Generalized Slit-Strips-Type Integral Boundary Conditions and Impulses

Lv¹,

Ahmad

et al. 2022

Fractal Fract

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In the current paper, we analyzed the existence and uniqueness of a solution for a coupled system of impulsive hybrid fractional differential equations involving ψ-Caputo fractional derivatives with generalized slit-strips-type integral boundary conditions. We also study the Ulam–Hyers stability for the considered system. For the existence and uniqueness of the solution, we use the Banach contraction principle. With the help of Schaefer’s fixed-point theorem and some assumptions, we also obtain at least one solution of the mentioned system. Finally, the main results are verified with an appropriate example.

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Fractional Differential Equations Involving Hadamard Fractional Derivatives with Nonlocal Multi-point Boundary Conditions

Cited by 10 publications

References 0 publications

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

Applicability of Darbo’s Fixed Point Theorem on the Existence of a Solution to Fractional Differential Equations of Sequential Type

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

Analysis of a Hybrid Coupled System of ψ-Caputo Fractional Derivatives with Generalized Slit-Strips-Type Integral Boundary Conditions and Impulses

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