Existence of solution of a nonlinear fractional dynamic equation with initial and boundary conditions on time scales

Gogoi, Bikash; Saha, Utpal Kumar; Hazarika, Bipan

doi:10.1007/s41478-023-00597-0

J Anal

2023

DOI: 10.1007/s41478-023-00597-0

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Existence of solution of a nonlinear fractional dynamic equation with initial and boundary conditions on time scales

Bikash Gogoi¹,

Utpal Kumar Saha²,

Bipan Hazarika³

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2024

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Cited by 3 publications

References 14 publications

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Fractional-Order Sequential Linear Differential Equations with Nabla Derivatives on Time Scales

Zhu,

Zhu

2024

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In this paper, we present a general theory for fractional-order sequential differential equations with Riemann–Liouville nabla derivatives and Caputo nabla derivatives on time scales. The explicit solution, in the case of constant coefficients, for both the homogeneous and the non-homogeneous problems, are given using the ∇-Mittag-Leffler function, Laplace transform method, operational method and operational decomposition method. In addition, we also provide some results about a solution to a new class of fractional-order sequential differential equations with convolutional-type variable coefficients using the Laplace transform method.

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Fractional-Order Sequential Linear Differential Equations with Nabla Derivatives on Time Scales

Zhu,

Zhu

2024

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A non-linear fractional neutral dynamic equations: existence and stability results on time scales

Nisar,

Anusha,

Ravichandran

2023

MATH

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<abstract><p>The outcomes of a nonlinear fractional neutral dynamic equation with initial conditions on time scales are examined in this work using the Riemann-Liouville nabla ($ \nabla $) derivative. The existence, uniqueness, and stability results for the solution are examined by using standard fixed point techniques. For the result illustration, an example is given along with the graph using MATLAB.</p></abstract>

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Results on generalized neutral fractional impulsive dynamic equation over time scales using nonlocal initial condition

Morsy,

Anusha,

Nisar

et al. 2024

MATH

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<abstract><p>This paper explored the existence and uniqueness of a neutral fractional impulsive dynamic equation over time scales that included nonlocal initial conditions and employed the Caputo-nabla derivative (C$ \nabla $D). The establishment of existence and uniqueness relies on the fine fixed point theorem. Furthermore, a comparison was conducted between the fractional order C$ \nabla $D and the Riemann-Liouville nabla derivative (RL$ \nabla $D) over time scales. Theoretical findings were substantiated through a numerical methodology, and an illustrative graph using MATLAB was presented for the provided example.</p></abstract>

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Existence of solution of a nonlinear fractional dynamic equation with initial and boundary conditions on time scales

Cited by 3 publications

References 14 publications

Fractional-Order Sequential Linear Differential Equations with Nabla Derivatives on Time Scales

Fractional-Order Sequential Linear Differential Equations with Nabla Derivatives on Time Scales

A non-linear fractional neutral dynamic equations: existence and stability results on time scales

Results on generalized neutral fractional impulsive dynamic equation over time scales using nonlocal initial condition

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