Manuel Fernández-Martínez holds an international PhD in Mathematics from UCLA. His research interests include fractal structures, fractal dimension, self-similar sets, computational applications of fractal dimension, and self-similar processes and their applications to finance.Miguel Ángel Sánchez-Granero is an Associate Professor at the Department of Mathematics, University of Almería, Spain. He is the author of a number of publications in international journals on asymmetric topology, self-similarity, fractal structures, and fractal dimension with application to financial series.Juan E. Trinidad Segovia, PhD, is a Full Professor of Finances at the Department of Economics and Business, University of Almería, Spain. His research interests include financial modelling, portfolio selection, CAPM and, most recently, applications of Statistical Mechanics to financial markets. He has published over 20 papers in peer-reviewed journals.Juan LuisGarcía Guirao is a Full Professor of Applied Mathematics at the Technical University of Cartagena, Spain. In 2011, at the age of 33, he became Spain’s youngest Full Professor of Mathematics. The author of more than 100 research papers and Editor in Chief of Applied Mathematics and Nonlinear Sciences, his work has been recognised with the 2017 NSP award for researchers younger than 40 years old, and with the 2017 JDEA best paper award.

• 1 Mathematical background.- 2 Box dimension type models.- 3 A middle definition between Hausdorff and box dimensions.- 4 Hausdorff dimension type models for fractal structures.

Manuel Fernández-Martínez holds an international PhD in Mathematics from UCLA. His research interests include fractal structures, fractal dimension, self-similar sets, computational applications of fractal dimension, and self-similar processes and their applications to finance.Miguel Ángel Sánchez-Granero is an Associate Professor at the Department of Mathematics, University of Almería, Spain. He is the author of a number of publications in international journals on asymmetric topology, self-similarity, fractal structures, and fractal dimension with application to financial series.Juan E. Trinidad Segovia, PhD, is a Full Professor of Finances at the Department of Economics and Business, University of Almería, Spain. His research interests include financial modelling, portfolio selection, CAPM and, most recently, applications of Statistical Mechanics to financial markets. He has published over 20 papers in peer-reviewed journals.Juan LuisGarcía Guirao is a Full Professor of Applied Mathematics at the Technical University of Cartagena, Spain. In 2011, at the age of 33, he became Spain’s youngest Full Professor of Mathematics. The author of more than 100 research papers and Editor in Chief of Applied Mathematics and Nonlinear Sciences, his work has been recognised with the 2017 NSP award for researchers younger than 40 years old, and with the 2017 JDEA best paper award.

• 1 Mathematical background.- 2 Box dimension type models.- 3 A middle definition between Hausdorff and box dimensions.- 4 Hausdorff dimension type models for fractal structures.

Manuel Fernández-Martínez holds an international PhD in Mathematics from UCLA. His research interests include fractal structures, fractal dimension, self-similar sets, computational applications of fractal dimension, and self-similar processes and their applications to finance.Miguel Ángel Sánchez-Granero is an Associate Professor at the Department of Mathematics, University of Almería, Spain. He is the author of a number of publications in international journals on asymmetric topology, self-similarity, fractal structures, and fractal dimension with application to financial series.Juan E. Trinidad Segovia, PhD, is a Full Professor of Finances at the Department of Economics and Business, University of Almería, Spain. His research interests include financial modelling, portfolio selection, CAPM and, most recently, applications of Statistical Mechanics to financial markets. He has published over 20 papers in peer-reviewed journals.Juan LuisGarcía Guirao is a Full Professor of Applied Mathematics at the Technical University of Cartagena, Spain. In 2011, at the age of 33, he became Spain’s youngest Full Professor of Mathematics. The author of more than 100 research papers and Editor in Chief of Applied Mathematics and Nonlinear Sciences, his work has been recognised with the 2017 NSP award for researchers younger than 40 years old, and with the 2017 JDEA best paper award.

• 1 Mathematical background.- 2 Box dimension type models.- 3 A middle definition between Hausdorff and box dimensions.- 4 Hausdorff dimension type models for fractal structures.