Existence Results for a Family of Equations of Fractional Resolvent

Abstract

This study deals with the presence and distinction of bounded m-solutions (type mild) for a family of generalized integral and differential equations of spot order with fractional resolvent and indefinite delay.

Solvability of fractional dynamic systems utilizing measure of noncompactness

“…Here h 11 (t) and h 21 (t) are simple functions, which are chosen as a prate of functions h 1 (t) and h 2 (t), respectively. Substituting (22) and (21) in (20) concludes that…”

“…Fractional calculus includes all fractional concepts, (operators) fractional formulas (equations, inequalities and inclusions) and fractional formal (logic concepts) (see [19,20,22,23,26]) can express the possessions of the history of materials. Practical problems take in classifications of the fractional operators (differential and integral) allowing the procedure of the entity and uniqueness of associations outcome based equity model.…”

“…. .By the construction of generalized homotopy perturbation(20) the coefficients of p powers are amounting to zero. Thus, we obtain an iterative process for numerical solution of(18).…”

Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials

“…The fractional calculus represents a powerful tool in applied mathematics to study a myriad of problems from different fields of science and engineering, with many break-through results found in mathematical physics, finance, hydrology, biophysics, thermodynamics, control theory, statistical mechanics, astrophysics, cosmology and bioengineering (Abbas et al 2015). Since the fractional calculus has attracted much more interest among mathematicians and other scientists, the solutions of the fractional integrodifferential equations have been studied frequently in recent years (Alkan & Hatipoglu 2017;Hamoud & Ghadle 2018a, 2018bIbrahim et al 2015;Kumar et al 2017;Ma & Huang 2014;Nemati et al 2016;Ordokhani & Dehestani 2016;Parand & Nikarya 2014;Pedas et al 2016;Shahooth et al 2016;Turmetov & Abdullaev 2017;Wang & Zhu 2016;Yi et al 2016). The methods that are used to find the solutions of the linear fractional Fredholm integro-differential equations are given as fractional pseudospectral integration matrices (Tang & Xu 2016), least squares with shifted Chebyshev polynomials Mohammed 2014), least squares method using Bernstein polynomials (Oyedepo et al 2016), fractional residual power series method (Syam 2017), Taylor matrix method (Gülsu et al 2013), reproducing kernel Hilbert space method (Bushnaq et al 2016), second kind Chebyshev wavelet method (Setia et al 2014), open Newton method (Al-Jamal & Rawashdeh 2009), modified Homotopy perturbation method (Elbeleze et al 2016), Sinc collocation method (Emiroglu 2015).…”