Advances in Boundary Value Problems for Fractional Differential Equations

Abstract

Fractional-order differential and integral operators and fractional differential equations have extensive applications in the mathematical modelling of real-world phenomena which occur in scientific and engineering disciplines such as physics, chemistry, biophysics, biology, medical sciences, financial economics, ecology, bioengineering, control theory, signal and image processing, aerodynamics, transport dynamics, thermodynamics, viscoelasticity, hydrology, statistical mechanics, electromagnetics, astrophysics, cosmology, and rheology [...]

Existence Theory and Stability Analysis to a Class of Hybrid Differential Equations using Confirmable Fractal Fractional Derivative

“…The two operators Confirmable Derivatives and Fractal Derivatives have prominent role in theory and applications [15]. Researchers have investigated various results for different problems of fractional calculus, we refer to [16,17,18,19]. Combining the two operators confirmable and fractal fractional derivatives were used recently for different problems.…”

Geraghty Type Contractions in Relational Metric Space with Applications to Fractional Differential Equations

“…Various authors have studied the solvability of certain classes of nonlinear FDE, e.g., Xiao [7], Zhang et al [8], Cevikel and Aksoy [9], Laoubi et al [10], Telli et al [11], Dincel et al [12], Area and Nieto [13], Jassim and Hussein [14], among others. In order to study the BVP (abbreviation of 'boundary value problem') for FDE, we refer the works of Jia et al [15], Su et al [16], Bouteraa and Benaicha [17], Zhang et al [18], Luca [19], Shah et al [20] and references therein. Very recently, Aljethi and Kiliçman [21] discussed the analytic properties of FDE and their applications to realistic data.…”