Fractional Neutral Integro-Differential Equations with Nonlocal Initial Conditions

Zhiyuan Yuan, Luyao Wang, Wenchang He, Ning Cai and Jia Mu ()
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Zhiyuan Yuan: School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
Luyao Wang: School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
Wenchang He: School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
Ning Cai: Department of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China
Jia Mu: School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China

Mathematics, 2024, vol. 12, issue 12, 1-14

Abstract: We primarily investigate the existence of solutions for fractional neutral integro-differential equations with nonlocal initial conditions, which are crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by using fixed-point theorems, we establish the existence of mild solutions under more relaxed conditions.

Keywords: fractional neutral integro-differential equations; resolvent family; probability density function; mild solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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