On solutions of fractal fractional differential equations

DOI10.3934/dcdss.2020421zbMath1481.34009OpenAlexW3048379687WikidataQ115219131 ScholiaQ115219131MaRDI QIDQ2230327

Ali Akgül, Abdon Atangana

Publication date: 17 September 2021

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2020421

zbMATH Keywords

Laplace transformMittag-Leffler kernelexponential decay kernelpower law kernelfractal fractional derivatives

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Mittag-Leffler functions and generalizations (33E12) Explicit solutions, first integrals of ordinary differential equations (34A05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Laplace transform (44A10) Fractional ordinary differential equations (34A08)

Related Items (7)

ON EXISTENCE AND STABILITY RESULTS FOR PANTOGRAPH FRACTIONAL BOUNDARY VALUE PROBLEMS ⋮ Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate ⋮ A ROBUST OPERATIONAL MATRIX OF NONSINGULAR DERIVATIVE TO SOLVE FRACTIONAL VARIABLE-ORDER DIFFERENTIAL EQUATIONS ⋮ The modified exponential function method for beta time fractional Biswas-Arshed equation ⋮ Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays ⋮ Global dynamics and bifurcation analysis of a fractional‐order SEIR epidemic model with saturation incidence rate ⋮ Master-slave synchronization for glucose-insulin metabolism of type-1 diabetic mellitus model based on new fractal-fractional order derivative

Cites Work

• Anomalous diffusion modeling by fractal and fractional derivatives
• Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system
• A novel method for a fractional derivative with non-local and non-singular kernel
• Sumudu transform in fractal calculus
• A new fractional modelling and control strategy for the outbreak of dengue fever
• Validity of fractal derivative to capturing chaotic attractors
• Solutions of the linear and nonlinear differential equations within the generalized fractional derivatives
• A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
• A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence

This page was built for publication: On solutions of fractal fractional differential equations