Dynamics and stability of ψ-fractional pantograph equations with boundary conditions | Zendy

Kamal Shah | Zendy; D. Vivek | Zendy; K. Kanagarajan | Zendy

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Dynamics and stability of ψ-fractional pantograph equations with boundary conditions

Author(s) -

Kamal Shah,

D. Vivek,

K. Kanagarajan

Publication year - 2020

Publication title -

boletim da sociedade paranaense de matemática

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.347

H-Index - 15

eISSN - 2175-1188

pISSN - 0037-8712

DOI - 10.5269/bspm.41154

Subject(s) - pantograph , mathematics , fractional calculus , stability (learning theory) , fixed point theorem , boundary value problem , mathematical analysis , fixed point , boundary (topology) , point (geometry) , dynamics (music) , type (biology) , derivative (finance) , computer science , geometry , physics , engineering , mechanical engineering , ecology , machine learning , biology , acoustics , financial economics , economics

This manuscript is devoted to obtain some adequate conditions for existence of at least one solution to fractional pantograph equation (FPE) involving the ψ -fractional derivative. The proposed problem is studied under some boundary conditions. Since stability is an important aspect of the qualitative theory. Therefore, we also discuss the Ulam-Hyers and Ulam-Hyers-Rassias type stabilities for the considered problem. Our results are based on some standard fixed point theorems. For the demonstration of our results, we provide an example. List of abbreviations: Boundary value problems (BVP), nonlinear fractional differential equations (NFDEs), fractional pantograph equation (FPE), Ulam-Hyers stability (UHS), Ulam-Hyers-Rassias stability (UHRS).

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