Cauchy problem for a high‐order loaded integro‐differential equation

The non-instantaneous condition is utilized in our study through the employment of the Cauchy problem in order to contract a system of nonlinear non-autonomous mixed-type integro-differential (ID) fractional evolution equations in infinite-dimensional Banach spaces. We reveal the existence of new mild solutions in the condition that the nonlinear function modifies approximately suitable, measure of non-compactness (MNC) form and local growth form using evolution classes along with fractional calculus (FC) theory as well as the fixed-point theorem with respect to k-set-contractive operator and MNC standard set. Consequently, as an example, we consider a fractional non-autonomous partial differential equation (PDE) with a homogeneous Dirichlet boundary condition and a non-instantaneous impulse condition. The conclusion of mild solution regarding the uniqueness and existence of a mild solution for a system with a probability density function and evolution classes is drawn with respect to the related domains.

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Non-Autonomous Fractional Evolution Equations With Non-Instantaneous Impulse Conditions of Order (1,2): A Cauchy Problem

Iqbal

Niazi

Khan

et al. 2022

Fractals

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Cauchy problem for a loaded hyperbolic equation with the Bessel operator

Baltaeva,

Khasanov

2024

Mathematica Slovaca

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This work is devoted to the study of the Cauchy problem for a loaded differential equation with the Bessel operator. When studying problems for loaded equations, the properties of Erdélyi-Kober operators are used as transformation operators concerning a relation. We obtain an explicit form of the solution to the Cauchy problem for a loaded one-dimensional differential equation. At the end of the work, we will show several examples on graphs.

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Cauchy problem for a high‐order loaded integro‐differential equation

Abstract: In the work was found an explicit formula of a solution of analog of a Cauchy problem for a loaded multidimensional partial differential equation of a higher order.

Cited by 2 publications

References 30 publications

Non-Autonomous Fractional Evolution Equations With Non-Instantaneous Impulse Conditions of Order (1,2): A Cauchy Problem

Non-Autonomous Fractional Evolution Equations With Non-Instantaneous Impulse Conditions of Order (1,2): A Cauchy Problem

Cauchy problem for a loaded hyperbolic equation with the Bessel operator

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