Theory and Modern Applications

# Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential Equations

Differential and integral calculus is undoubtedly one of the most important concepts of mathematics and appears naturally in numerous scientific problems, which have been widely applied in physics, chemical technology, optimal control, finance, signal processing, etc. and are modeled by ordinary or partial difference and differential equations.

In recent years, it was observed that many real-world phenomena cannot be modeled by ordinary or partial differential equations or standard difference equations defined via the classical derivatives and integrals. In fact, these problems followed the appearance of fractional calculus (fractional derivatives and integrals), intended to handle the problems for which the classical calculus was insufficient. Together with the development and progress in fractional calculus, the theory and applications of ordinary and partial differential equations with fractional derivatives became one of the most studied topics in applied mathematics. The wide application potential of fractional differential equations in many fields of science has been underlined by a huge number of articles, books, and scientific events on the subject.

Fixed point theory on the other hand, is a very strong mathematical tool to establish the existence and uniqueness of almost all problems modeled by nonlinear relations. Consequently, existence and uniqueness problems of fractional differential equations are studied by means of fixed point theory. For about a century, fixed point theory has begun to take shape, and developed rapidly. Due to its applications, fixed point theory is highly appreciated and continues to be explored. Besides, this theory can be applied in many types of spaces, such as abstract spaces, metric spaces, and Sobolev spaces. This feature of fixed point theory makes is very valuable in studying numerous problems of practical sciences modeled by fractional ordinary and partial differential and difference equations.

This special issue will collect the ideas for theoretical advances on fixed point theory and applications to fractional ordinary and partial difference and differential equations. We welcome both original research articles and articles discussing the current situation. Potential topics include, but are not limited to the following:

• Fractional-order difference equations
• Fractional differentialâ€“difference equations
• Fractional inequalities and their applications in fractional difference equations
• Fixed point theory and applications
• Topological fixed-point theory
• Fractional ordinary/partial differential equations
• Fractional stochastic ordinary/partial differential equations
• Nonlinear problems with fixed point theory approaches
• Controllability problems for nonlinear systems
• Impulsive differential equations

Erdal Karapinar, Cankaya University, Turkey and China Medical University, Taiwan, erdal.karapinar@cankaya.edu.tr

Guest editors:

TomÃ¡s Caraballo, Universidad de Sevilla, Spain, caraball@us.es

Inci Erhan, Atilim University, Turkey, incierhan@gmail.com

Nguyen Huy Tuan, University of Science, Viet Nam National University, Viet Nam, nhtuan@hcmus.edu.vn

Important dates:

Opened submission date: 1 January 2021

Submission Instructions:
Before submitting your manuscript, please ensure you have carefully read the submission guidelines for Advances in Difference Equations. The complete manuscript should be submitted through the journal's submission system. To ensure that you submit to the correct thematic series please select the appropriate thematic series in the drop-down menu upon submission. In addition, indicate within your cover letter that you wish your manuscript to be considered as part of the thematic series on coronavirus/COVID-19. All submissions will undergo rigorous peer-review and accepted articles will be published in the journal as a collection.

Submissions will also benefit from the usual advantages of open access publication:

Rapid publication: Online submission, electronic peer review, and production make the process of publishing your article simple and efficient

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Authors retain copyright, licensing the article under a Creative Commons license: articles can be freely redistributed and reused as long as the article is correctly attributed.