Abstract
In this paper, we study the solvability of a class of nonlinear multiorder Caputo fractional differential equations with integral and antiperiodic boundary conditions. By using some fixed point theorems including the Banach contraction mapping principle and Schaefer’s fixed point theorem, we obtain new existence and uniqueness results for our given problem. Also, we give some examples to illustrate our main results.
Highlights
Fractional calculus has a history of several hundred years, and many valuable results that have contributed to the development of mathematical theories and their application to practice have been created during its historical process
Fractional differential equations are one of the powerful means to model and solve scientific and technological problems that have been arisen in physics, chemistry, biology, mechanics, and many other fields, and it has developed more and more in-depth
Boundary value problems of fractional differential equations are often used as mathematical models for many phenomena in a variety of physical, biological, mechanical, and chemical studies such as analysis of turbulent flow, simulation of chemical reaction, and image processing technique
Summary
Fractional calculus has a history of several hundred years, and many valuable results that have contributed to the development of mathematical theories and their application to practice have been created during its historical process (see [1]). Ð2Þ uð0Þ = −uðTÞ, where λi ∈ R, i = 0, 1, ⋯, n, λn ≠ 0, 0 ≤ α0 < α1
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