Abstract
In the existing study, we investigate the criteria of existence of solution for relatively new categories of φ-Caputo fractional differential equations and inclusions problems equipped with nonlocal φ-integral boundary conditions. In order to achieve the desired goal, we use α–ψ-contractive mappings and the theory of approximate endpoint. In the final stage, we exhibit some examples to provide the illustrations of our theoretical findings.
Highlights
The calculus of arbitrary order, the fractional order calculus, has been considered as the most useful branch of mathematics in various applied sciences and engineering
Our work in the present research is novel in introducing a new development of two φ-fractional differential problems equipped with nonlocal boundary conditions and constructing new operators which belong to a new class of core functions
6 Conclusion A number of natural phenomena emerging in science and technology are modeled by fractional differential equations (FDEs)
Summary
The calculus of arbitrary order, the fractional order calculus, has been considered as the most useful branch of mathematics in various applied sciences and engineering. Our work in the present research is novel in introducing a new development of two φ-fractional differential problems equipped with nonlocal boundary conditions and constructing new operators which belong to a new class of core functions. The α-admissible and α–ψ-counteractive maps are two major functions of this category Using such a broad class of functions defined on space admitting properties (P1) and (P2), we investigate the existence criteria of two BVPs (1) and (2). We derive another condition of the existence of solutions from the (AEP)property for the assumed multifunction and the aid of endpoint notion. The last section is devoted to the illustration of results presented in Sects. 3 and 4 in terms of numerical examples
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