An Iterative Method for Solving a Class of Fractional Functional Differential Equations with “Maxima”

In the present work, we deal with nonlinear fractional differential equations with “maxima” and deviating arguments. The nonlinear part of the problem under consideration depends on the maximum values of the unknown function taken in time-dependent intervals. Proceeding by an iterative approach, we obtain the existence and uniqueness of the solution, in a context that does not fit within the framework of fixed point theory methods for the self-mappings, frequently used in the study of such problems. An example illustrating our main result is also given.

• fractional functional differential equations
• deviating arguments
• nonlinear fractional differential equations
• iterative methods
• existence and uniqueness of solutions

• Nonlinear Differential Equations Analysis
• Fuzzy Systems and Optimization
• Fractional Differential Equations Solutions
• fractional functional differential equations
• deviating arguments
• nonlinear fractional differential equations
• iterative methods
• existence and uniqueness of solutions
• Applied Mathematics
• Statistics and Probability
• Modeling and Simulation
• Mathematics