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Fractional differential equations with nonlocal (parametric type) anti-periodic boundary conditions

Agarwal Ravi P. (aDepartment of Mathematics, Texas A&M University, Kingsville, USA + King Abdulaziz University, Faculty of Science, Department of Mathematics, NAAM-Research Group, Jeddah , Saudi Arabia)
Ahmad Bashir (King Abdulaziz University, Faculty of Science, Department of Mathematics, NAAM-Research Group, Jeddah, Saudi Arabia)
Nieto Juan J. (Universidad de Santiago de Compostela, Facultad de Matemáticas, Santiago de Compostela, Spain + King Abdulaziz University, Faculty of Science, Department of Mathematics, NAAM-Research Group, Jeddah, Saudi Arabia)

In this paper, we introduce a new concept of nonlocal anti-periodic boundary conditions and solve fractional and sequential fractional differential equations supplemented with these conditions. The anti-periodic boundary conditions involve a nonlocal intermediate point together with one of the fixed end points of the interval under consideration, and accounts for a flexible situation concerning anti-periodic phenomena. The existence results for the given problems are obtained with the aid of standard fixed point theorems. Some examples illustrating the main results are also discussed. The paper concludes with several interesting observations.

Keywords: fractional differential equations, nonlocal, anti-periodic boundary conditions, existence, fixed point theorem