Abstract
This paper investigates the existence of solutions for nonlinear fractional differential equations with m-point Erdelyi-Kober fractional integral boundary conditions on an infinite interval via the Leray-Schauder nonlinear alternative and the Banach contraction principle. Some examples illustrating the main results are also presented.
Highlights
1 Introduction Fractional differential equations arise in many engineering and scientific disciplines as the mathematical models of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, electrical circuits, biology, control theory, fitting of experimental data, and so on, and involves derivatives of fractional order
This is the main advantage of fractional differential equations in comparison with classical integer-order models
Motivated by the above papers, in this article, we study a new class of boundary value problems on fractional differential equations with m-point Erdélyi-Kober fractional integral boundary conditions on an infinite interval of the form
Summary
Fractional differential equations arise in many engineering and scientific disciplines as the mathematical models of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, electrical circuits, biology, control theory, fitting of experimental data, and so on, and involves derivatives of fractional order. Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes This is the main advantage of fractional differential equations in comparison with classical integer-order models. Zhao and Ge [ ] studied the existence of unbounded solutions for the following boundary value problem on the infinite interval: Dα u(t) + f t, u(t) = , < α ≤ , t ∈ [ , ∞),. Zhang et al [ ] studied the existence of nonnegative solutions for the following boundary value problem for fractional differential equations with nonlocal boundary conditions on unbounded domains:. Motivated by the above papers, in this article, we study a new class of boundary value problems on fractional differential equations with m-point Erdélyi-Kober fractional integral boundary conditions on an infinite interval of the form. From the definition of the Riemann-Liouville fractional derivative and integral, we can obtain the following lemmas.
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