Abstract
In this research work, we study a new class of ψ -Hilfer hybrid fractional integro-differential boundary value problems with nonlocal boundary conditions. Existence results are established for single and multivalued cases, by using suitable fixed-point theorems for the product of two single or multivalued operators. Examples illustrating the main results are also constructed.
Highlights
Some real-world problems in physics, mechanics, and other fields can be described better with the help of fractional differential equations
We investigate the existence of solutions for the following inclusion ψ-Hilfer fractional hybrid integro-differential equations with nonlocal boundary conditions of the form
We present an example of ψ-Hilfer hybrid fractional integro-differential boundary value problem to illustrate our main result
Summary
Some real-world problems in physics, mechanics, and other fields can be described better with the help of fractional differential equations. >: xð0Þ = xð1Þ = 0, ð3Þ where Dq is the Riemann-Liouville fractional derivative of order 1 < q < 2,f ∈ Cð1⁄20, 1 × R, R \ f0gÞ, and g ∈ Cð1⁄20, 1 × R, RÞ: In [20], the authors studied the existence of solutions for a nonlocal boundary value problem of hybrid fractional integro-differential equations given by. In [31], an initial value problem was discussed for hybrid fractional differential equations involving ψ-Hilfer fractional derivative of the form 8 >>>
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