Applying new fixed point theorems on fractional and ordinary differential equations

DOI10.1186/s13662-019-2354-3zbMath1487.54065OpenAlexW2977811462WikidataQ127172974 ScholiaQ127172974MaRDI QIDQ2141939

Fahd Jarad, Erdal Karapınar, Thabet Abdeljawad

Publication date: 25 May 2022

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-019-2354-3

zbMATH Keywords

fractional differential equationscontractionsweakly contractive mappings

Mathematics Subject Classification ID

Fixed-point and coincidence theorems (topological aspects) (54H25) Special maps on metric spaces (54E40) Fractional ordinary differential equations (34A08)

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Cites Work

• Unnamed Item
• Unnamed Item
• Two fractional derivative inclusion problems via integral boundary condition
• The existence of solutions for a nonlinear mixed problem of singular fractional differential equations
• Tempered fractional calculus
• Meir-Keeler \(\alpha\)-contractive fixed and common fixed point theorems
• Common fixed points of generalized Meir-Keeler \(\alpha\)-contractions
• Fixed point theorems for \(\alpha\)-Geraghty contraction type maps in metric spaces
• Fixed point theorems for \(\alpha\)-\(\psi\)-contractive type mappings
• Generalized \(\alpha\)-\(\psi\) contractive type mappings and related fixed point theorems with applications
• On conformable fractional calculus
• Best proximity points for generalized \(\alpha\)-\(\phi\)-Geraghty proximal contraction mappings and its applications
• A generalisation of contraction principle in metric spaces
• An extension of Banach contraction principle through rational expression
• Some unique fixed point theorems
• Recent applications of fractional calculus to science and engineering
• Monotonicity results for fractional difference operators with discrete exponential kernels
• On fractional derivatives with exponential kernel and their discrete versions
• Some theorems on weakly contractive maps.
• Best proximity points of generalized almost \(\psi\)-Geraghty contractive non-self-mappings
• A note on `\(\psi\)-Geraghty type contractions'
• On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative
• On \(\alpha\)-\(\psi\)-Meir-Keeler contractive mappings
• A new definition of fractional derivative
• Some new fixed point theorems for \(\alpha\)-Geraghty contraction type maps in metric spaces
• A generalization for the best proximity point of Geraghty-contractions
• On coupled systems of time-fractional differential problems by using a new fractional derivative
• Well-posedness and numerical algorithm for the tempered fractional differential equations
• Some existence results on nonlinear fractional differential equations
• A discussion on "α-ψ-Geraghty contraction type mappings"
• Fractional operators with generalized Mittag-Leffler kernels and their iterated differintegrals
• Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel
• On Nonlinear Contractions
• Decomposition of an Integral Operator by Use of Mikusiński Calculus
• On Contractive Mappings