Manuscript Topics

The importance of initial and boundary value problems of different kinds of differential equations (ordinary, functional, fractional, q-difference, partial, etc.) is well-recognized in view of their extensive applications in applied sciences and engineering. Much of the literature on the topic deals with classical boundary conditions. However, in order to model the physical problems involving the data available at arbitrary interior points or finite many segments of the given domain, one needs to apply the concept of nonlocal conditions. In case of arbitrarily shaped domain, integral boundary conditions act as more realistic and practical tools. There do exist numerous advanced and efficient methods to deal with the existence of solutions to differential equations. In particular, the tools of fixed-point theory are found to be of great utility in obtaining the existence criteria for solutions to nonlinear initial and boundary value problems. During the last few decades, the subject of fractional-order initial and boundary value problems received overwhelming interest since the methods of fractional calculus led to the revolution in the field mathematical modeling.

The aim of this Special Issue is to enhance and enrich the literature on initial and boundary value problems of differential equations in a broad sense.

Potential topics related to the study of initial and boundary value problems include, but are not limited to

• Existence, uniqueness and multiplicity results
• Qualitative properties (positivity, oscillation, asymptotic behavior, stability, etc.) of solutions
• Approximation of solutions
• Analytic and numerical methods
• Real-world applications

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