On the Caputo-Hadamard fractional IVP with variable order using the upper-lower solutions technique
Copyright policy )On the Caputo-Hadamard fractional IVP with variable order using the upper-lower solutions technique
<abstract><p>This paper studies the existence of solutions for Caputo-Hadamard fractional nonlinear differential equations of variable order (CHFDEVO). We obtain some needed conditions for this purpose by providing an auxiliary constant order system of the given CHFDEVO. In other words, with the help of piece-wise constant order functions on some continuous subintervals of a partition, we convert the main variable order initial value problem (IVP) to a constant order IVP of the Caputo-Hadamard differential equations. By calculating and obtaining equivalent solutions in the form of a Hadamard integral equation, our results are established with the help of the upper-lower-solutions method. Finally, a numerical example is presented to express the validity of our results.</p></abstract>
- China Medical University China (People's Republic of)
- China Medical University Hospital Taiwan
- Université IBN Khaldoun Tiaret Algeria
- University of the Basque Country Spain
- Siirt University Turkey
Fractional Differential Equations, Economics, existence results, Caputo-Hadamard fractional derivative, fractional variable order, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Differential equation, QA1-939, FOS: Mathematics, Variable (mathematics), upper-lower solutions, Anomalous Diffusion Modeling and Analysis, Hadamard transform, Order (exchange), Impulsive Differential Equations, Applied Mathematics, Bifurcations in Planar Polynomial Systems, Physics, Partition (number theory), Applied mathematics, Computer science, Programming language, Fractional Derivatives, Initial value problem, Combinatorics, Modeling and Simulation, Physical Sciences, Nonlinear system, Geometry and Topology, caputo-hadamard fractional derivative, Mathematics, Finance, Constant (computer programming)
Fractional Differential Equations, Economics, existence results, Caputo-Hadamard fractional derivative, fractional variable order, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Differential equation, QA1-939, FOS: Mathematics, Variable (mathematics), upper-lower solutions, Anomalous Diffusion Modeling and Analysis, Hadamard transform, Order (exchange), Impulsive Differential Equations, Applied Mathematics, Bifurcations in Planar Polynomial Systems, Physics, Partition (number theory), Applied mathematics, Computer science, Programming language, Fractional Derivatives, Initial value problem, Combinatorics, Modeling and Simulation, Physical Sciences, Nonlinear system, Geometry and Topology, caputo-hadamard fractional derivative, Mathematics, Finance, Constant (computer programming)
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